{"id":13772,"date":"2017-07-14T17:09:06","date_gmt":"2017-07-14T17:09:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=13772"},"modified":"2020-07-02T05:42:53","modified_gmt":"2020-07-02T05:42:53","slug":"problem-set-the-language-of-algebra","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/problem-set-the-language-of-algebra\/","title":{"raw":"Problem Set: The Language of Algebra","rendered":"Problem Set: The Language of Algebra"},"content":{"raw":"

Using the Language of Algebra<\/h2>\r\n

Use Variables and Algebraic Symbols<\/h3>\r\nIn the following exercises, translate from algebraic notation to words.\r\n
    \r\n \t
  1. [latex]16 - 9[\/latex]\r\n[reveal-answer q=\"747161\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"747161\"]16 minus 9, the difference of sixteen and nine[\/hidden-answer]<\/li>\r\n \t
  2. [latex]25 - 7[\/latex]<\/li>\r\n \t
  3. [latex]5\\cdot 6[\/latex]\r\n[reveal-answer q=\"647507\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"647507\"]5 times 6, the product of five and six[\/hidden-answer]<\/li>\r\n \t
  4. [latex]3\\cdot 9[\/latex]<\/li>\r\n \t
  5. [latex]28\\div 4[\/latex]\r\n[reveal-answer q=\"767306\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"767306\"]28 divided by 4, the quotient of twenty-eight and four[\/hidden-answer]<\/li>\r\n \t
  6. [latex]45\\div 5[\/latex]<\/li>\r\n \t
  7. [latex]x+8[\/latex]\r\n[reveal-answer q=\"462120\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"462120\"]x plus 8, the sum of x and eight[\/hidden-answer]<\/li>\r\n \t
  8. [latex]x+11[\/latex]<\/li>\r\n \t
  9. [latex]\\left(2\\right)\\left(7\\right)[\/latex]\r\n[reveal-answer q=\"864259\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"864259\"]2 times 7, the product of two and seven[\/hidden-answer]<\/li>\r\n \t
  10. [latex]\\left(4\\right)\\left(8\\right)[\/latex]<\/li>\r\n \t
  11. [latex]14<21[\/latex]\r\n[reveal-answer q=\"669214\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"669214\"]fourteen is less than twenty-one[\/hidden-answer]<\/li>\r\n \t
  12. [latex]17<35[\/latex]<\/li>\r\n \t
  13. [latex]36\\ge 19[\/latex]\r\n[reveal-answer q=\"778121\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"778121\"]thirty-six is greater than or equal to nineteen[\/hidden-answer]<\/li>\r\n \t
  14. [latex]42\\ge 27[\/latex]<\/li>\r\n \t
  15. [latex]3n=24[\/latex]\r\n[reveal-answer q=\"230070\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"230070\"]3 times n equals 24, the product of three and n equals twenty-four[\/hidden-answer]<\/li>\r\n \t
  16. [latex]6n=36[\/latex]<\/li>\r\n \t
  17. [latex]y - 1>6[\/latex]\r\n[reveal-answer q=\"419025\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"419025\"]y minus 1 is greater than 6, the difference of y and one is greater than six[\/hidden-answer]<\/li>\r\n \t
  18. [latex]y - 4>8[\/latex]<\/li>\r\n \t
  19. [latex]2\\le 18\\div 6[\/latex]\r\n[reveal-answer q=\"801781\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"801781\"]2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six[\/hidden-answer]<\/li>\r\n \t
  20. [latex]3\\le 20\\div 4[\/latex]<\/li>\r\n \t
  21. [latex]a\\ne 7\\cdot 4[\/latex]\r\n[reveal-answer q=\"438128\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"438128\"]a is not equal to 7 times 4, a is not equal to the product of seven and four[\/hidden-answer]<\/li>\r\n \t
  22. [latex]a\\ne 1\\cdot 12[\/latex]<\/li>\r\n<\/ol>\r\n

    Identify<\/strong> Expressions and Equations<\/strong><\/h3>\r\nIn the following exercises, determine if each is an expression or an equation.\r\n
      \r\n \t
    1. [latex]9\\cdot 6=54[\/latex]\r\n[reveal-answer q=\"685017\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"685017\"]equation[\/hidden-answer]<\/li>\r\n \t
    2. [latex]7\\cdot 9=63[\/latex]<\/li>\r\n \t
    3. [latex]5\\cdot 4+3[\/latex]\r\n[reveal-answer q=\"762402\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"762402\"]expression[\/hidden-answer]<\/li>\r\n \t
    4. [latex]6\\cdot 3+5[\/latex]<\/li>\r\n \t
    5. [latex]x+7[\/latex]\r\n[reveal-answer q=\"660093\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"660093\"]expression[\/hidden-answer]<\/li>\r\n \t
    6. [latex]x+9[\/latex]<\/li>\r\n \t
    7. [latex]y - 5=25[\/latex]\r\n[reveal-answer q=\"396879\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"396879\"]equation[\/hidden-answer]<\/li>\r\n \t
    8. [latex]y - 8=32[\/latex]<\/li>\r\n<\/ol>\r\n

      Simplify Expressions with Exponents<\/h3>\r\nIn the following exercises, write in exponential form.\r\n
        \r\n \t
      1. [latex]3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3[\/latex]\r\n[reveal-answer q=\"291375\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"291375\"]37<\/sup>[\/hidden-answer]<\/li>\r\n \t
      2. [latex]4\\cdot 4\\cdot 4\\cdot 4\\cdot 4\\cdot 4[\/latex]<\/li>\r\n \t
      3. [latex]x\\cdot x\\cdot x\\cdot x\\cdot x[\/latex]\r\n[reveal-answer q=\"502416\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"502416\"]x5<\/sup>[\/hidden-answer]<\/li>\r\n \t
      4. [latex]y\\cdot y\\cdot y\\cdot y\\cdot y\\cdot y[\/latex]<\/li>\r\n<\/ol>\r\n

        Simplify Expressions with Exponents<\/h3>\r\nIn the following exercises, write in expanded form.\r\n
          \r\n \t
        1. [latex]{5}^{3}[\/latex]\r\n[reveal-answer q=\"859837\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"859837\"]125[\/hidden-answer]<\/li>\r\n \t
        2. [latex]{8}^{3}[\/latex]<\/li>\r\n \t
        3. [latex]{2}^{8}[\/latex]\r\n[reveal-answer q=\"621722\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"621722\"]256[\/hidden-answer]<\/li>\r\n \t
        4. [latex]{10}^{5}[\/latex]<\/li>\r\n<\/ol>\r\n

          Simplify<\/strong> Expressions Using the Order of Operations<\/strong><\/h3>\r\nIn the following exercises, simplify.\r\n
            \r\n \t
          1. [latex]3+8\\cdot 5[\/latex]\r\n[reveal-answer q=\"30785\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"30785\"]43[\/hidden-answer]<\/li>\r\n \t
          2. [latex]\\text{(3+8)}\\cdot \\text{5}[\/latex]\r\n[reveal-answer q=\"24469\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"24469\"]55[\/hidden-answer]<\/li>\r\n \t
          3. [latex]2+6\\cdot 3[\/latex]<\/li>\r\n \t
          4. [latex]\\text{(2+6)}\\cdot \\text{3}[\/latex]<\/li>\r\n \t
          5. [latex]{2}^{3}-12\\div \\left(9 - 5\\right)[\/latex]\r\n[reveal-answer q=\"134059\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"134059\"]5[\/hidden-answer]<\/li>\r\n \t
          6. [latex]{3}^{2}-18\\div \\left(11 - 5\\right)[\/latex]<\/li>\r\n \t
          7. [latex]3\\cdot 8+5\\cdot 2[\/latex]\r\n[reveal-answer q=\"785732\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"785732\"]34[\/hidden-answer]<\/li>\r\n \t
          8. [latex]4\\cdot 7+3\\cdot 5[\/latex]<\/li>\r\n \t
          9. [latex]2+8\\left(6+1\\right)[\/latex]\r\n[reveal-answer q=\"778506\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"778506\"]58[\/hidden-answer]<\/li>\r\n \t
          10. [latex]4+6\\left(3+6\\right)[\/latex]<\/li>\r\n \t
          11. [latex]4\\cdot 12\/8[\/latex]\r\n[reveal-answer q=\"746255\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"746255\"]6[\/hidden-answer]<\/li>\r\n \t
          12. [latex]2\\cdot 36\/6[\/latex]<\/li>\r\n \t
          13. [latex]6+10\/2+2[\/latex]\r\n[reveal-answer q=\"625759\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"625759\"]13[\/hidden-answer]<\/li>\r\n \t
          14. [latex]9+12\/3+4[\/latex]<\/li>\r\n \t
          15. [latex]\\left(6+10\\right)\\div \\left(2+2\\right)[\/latex]\r\n[reveal-answer q=\"296071\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"296071\"]4[\/hidden-answer]<\/li>\r\n \t
          16. [latex]\\left(9+12\\right)\\div \\left(3+4\\right)[\/latex]<\/li>\r\n \t
          17. [latex]20\\div 4+6\\cdot 5[\/latex]\r\n[reveal-answer q=\"575023\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"575023\"]35[\/hidden-answer]<\/li>\r\n \t
          18. [latex]33\\div 3+8\\cdot 2[\/latex]<\/li>\r\n \t
          19. [latex]20\\div \\left(4+6\\right)\\cdot 5[\/latex]\r\n[reveal-answer q=\"401536\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"401536\"]10[\/hidden-answer]<\/li>\r\n \t
          20. [latex]33\\div \\left(3+8\\right)\\cdot 2[\/latex]<\/li>\r\n \t
          21. [latex]{4}^{2}+{5}^{2}[\/latex]\r\n[reveal-answer q=\"675422\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"675422\"]41[\/hidden-answer]<\/li>\r\n \t
          22. [latex]{3}^{2}+{7}^{2}[\/latex]<\/li>\r\n \t
          23. [latex]{\\left(4+5\\right)}^{2}[\/latex]\r\n[reveal-answer q=\"18876\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"18876\"]81[\/hidden-answer]<\/li>\r\n \t
          24. [latex]{\\left(3+7\\right)}^{2}[\/latex]<\/li>\r\n \t
          25. [latex]3\\left(1+9\\cdot 6\\right)-{4}^{2}[\/latex]\r\n[reveal-answer q=\"528347\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"528347\"]149[\/hidden-answer]<\/li>\r\n \t
          26. [latex]5\\left(2+8\\cdot 4\\right)-{7}^{2}[\/latex]<\/li>\r\n \t
          27. [latex]2\\left[1+3\\left(10 - 2\\right)\\right][\/latex]\r\n[reveal-answer q=\"209345\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"209345\"]50[\/hidden-answer]<\/li>\r\n \t
          28. [latex]5\\left[2+4\\left(3 - 2\\right)\\right][\/latex]<\/li>\r\n<\/ol>\r\n
            \r\n

            Everyday Math<\/h3>\r\n

            Basketball<\/h4>\r\nIn the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol [latex]\\text{(=},\\text{<},\\text{>)}[\/latex].\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Spurs<\/strong><\/th>\r\nHeight<\/strong><\/th>\r\n<\/th>\r\nHeat<\/strong><\/th>\r\nHeight<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            Tim Duncan<\/td>\r\n83\"<\/td>\r\n<\/td>\r\nRashard Lewis<\/td>\r\n82\"<\/td>\r\n<\/tr>\r\n
            Boris Diaw<\/td>\r\n80\"<\/td>\r\nLeBron James<\/td>\r\n80\"<\/td>\r\n<\/tr>\r\n
            Kawhi Leonard<\/td>\r\n79\"<\/td>\r\nChris Bosh<\/td>\r\n83\"<\/td>\r\n<\/tr>\r\n
            Tony Parker<\/td>\r\n74\"<\/td>\r\nDwyane Wade<\/td>\r\n76\"<\/td>\r\n<\/tr>\r\n
            Danny Green<\/td>\r\n78\"<\/td>\r\nRay Allen<\/td>\r\n77\"<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
              \r\n \t
            1. Height of Tim Duncan____Height of Rashard Lewis<\/li>\r\n \t
            2. Height of Boris Diaw____Height of LeBron James<\/li>\r\n \t
            3. Height of Kawhi Leonard____Height of Chris Bosh<\/li>\r\n \t
            4. Height of Tony Parker____Height of Dwyane Wade<\/li>\r\n \t
            5. Height of Danny Green____Height of Ray Allen<\/li>\r\n<\/ol>\r\n

              Elevation<\/h4>\r\nIn Colorado there are more than [latex]50[\/latex] mountains with an elevation of over [latex]14,000\\text{ feet.}[\/latex] The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
              Mountain<\/th>\r\nElevation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
              Mt. Elbert<\/td>\r\n14,433'<\/td>\r\n<\/tr>\r\n
              Mt. Massive<\/td>\r\n14,421'<\/td>\r\n<\/tr>\r\n
              Mt. Harvard<\/td>\r\n14,420'<\/td>\r\n<\/tr>\r\n
              Blanca Peak<\/td>\r\n14,345'<\/td>\r\n<\/tr>\r\n
              La Plata Peak<\/td>\r\n14,336'<\/td>\r\n<\/tr>\r\n
              Uncompahgre Peak<\/td>\r\n14,309'<\/td>\r\n<\/tr>\r\n
              Crestone Peak<\/td>\r\n14,294'<\/td>\r\n<\/tr>\r\n
              Mt. Lincoln<\/td>\r\n14,286'<\/td>\r\n<\/tr>\r\n
              Grays Peak<\/td>\r\n14,270'<\/td>\r\n<\/tr>\r\n
              Mt. Antero<\/td>\r\n14,269'<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nElevation of La Plata Peak____Elevation of Mt. Antero\r\nElevation of Blanca Peak____Elevation of Mt. Elbert\r\nElevation of Gray\u2019s Peak____Elevation of Mt. Lincoln\r\nElevation of Mt. Massive____Elevation of Crestone Peak\r\nElevation of Mt. Harvard____Elevation of Uncompahgre Peak\r\n\r\n<\/div>\r\n
              \r\n

              Writing Exercises<\/h3>\r\nExplain the difference between an expression and an equation.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nWhy is it important to use the order of operations to simplify an expression?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

              Evaluating, Simplifying, and Translating Algebraic Expressions<\/h2>\r\n

              Evaluate Algebraic Expressions<\/h3>\r\nIn the following exercises, evaluate the expression for the given value.\r\n
                \r\n \t
              1. [latex]7x+8\\text{ when }x=2[\/latex]\r\n[reveal-answer q=\"345087\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"345087\"]22[\/hidden-answer]<\/li>\r\n \t
              2. [latex]9x+7\\text{ when }x=3[\/latex]<\/li>\r\n \t
              3. [latex]5x - 4\\text{ when }x=6[\/latex]\r\n[reveal-answer q=\"435745\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"435745\"]26[\/hidden-answer]<\/li>\r\n \t
              4. \u00a0[latex]8x - 6\\text{ when }x=7[\/latex]<\/li>\r\n \t
              5. [latex]{x}^{2}\\text{ when }x=12[\/latex]\r\n[reveal-answer q=\"362\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"362\"]144[\/hidden-answer]<\/li>\r\n \t
              6. [latex]{x}^{3}\\text{ when }x=5[\/latex]<\/li>\r\n \t
              7. [latex]{x}^{5}\\text{ when }x=2[\/latex]\r\n[reveal-answer q=\"461036\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"461036\"]32[\/hidden-answer]<\/li>\r\n \t
              8. [latex]{x}^{4}\\text{ when }x=3[\/latex]<\/li>\r\n \t
              9. [latex]{3}^{x}\\text{ when }x=3[\/latex]\r\n[reveal-answer q=\"972503\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"972503\"]27[\/hidden-answer]<\/li>\r\n \t
              10. [latex]{4}^{x}\\text{ when }x=2[\/latex]<\/li>\r\n \t
              11. [latex]{x}^{2}+3x - 7\\text{ when }x=4[\/latex]\r\n[reveal-answer q=\"142848\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"142848\"]21[\/hidden-answer]<\/li>\r\n \t
              12. [latex]{x}^{2}+5x - 8\\text{ when }x=6[\/latex]<\/li>\r\n \t
              13. [latex]2x+4y - 5\\text{ when }x=7,y=8[\/latex]\r\n[reveal-answer q=\"623836\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"623836\"]41[\/hidden-answer]<\/li>\r\n \t
              14. [latex]6x+3y - 9\\text{ when }x=6,y=9[\/latex]<\/li>\r\n \t
              15. [latex]{\\left(x-y\\right)}^{2}\\text{ when }x=10,y=7[\/latex]\r\n[reveal-answer q=\"323803\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"323803\"]9[\/hidden-answer]<\/li>\r\n \t
              16. [latex]{\\left(x+y\\right)}^{2}\\text{ when }x=6,y=9[\/latex]\r\n[reveal-answer q=\"738800\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"738800\"]225[\/hidden-answer]<\/li>\r\n \t
              17. [latex]{a}^{2}+{b}^{2}\\text{ when }a=3,b=8[\/latex]\r\n[reveal-answer q=\"268080\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"268080\"]73[\/hidden-answer]<\/li>\r\n \t
              18. [latex]{r}^{2}-{s}^{2}\\text{ when }r=12,s=5[\/latex]<\/li>\r\n \t
              19. [latex]2l+2w\\text{ when }l=15,w=12[\/latex]\r\n[reveal-answer q=\"295905\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"295905\"]54[\/hidden-answer]<\/li>\r\n \t
              20. [latex]2l+2w\\text{ when }l=18,w=14[\/latex]<\/li>\r\n<\/ol>\r\n

                Identify Terms, Coefficients, and Like Terms<\/h3>\r\nIn the following exercises, list the terms in the given expression.\r\n
                  \r\n \t
                1. [latex]15{x}^{2}+6x+2[\/latex]\r\n[reveal-answer q=\"250881\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"250881\"]15x2, 6x, 2[\/hidden-answer]<\/li>\r\n \t
                2. [latex]11{x}^{2}+8x+5[\/latex]<\/li>\r\n \t
                3. [latex]10{y}^{3}+y+2[\/latex]\r\n[reveal-answer q=\"378199\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"378199\"]10y3, y, 2[\/hidden-answer]<\/li>\r\n \t
                4. [latex]9{y}^{3}+y+5[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, identify the coefficient of the given term.\r\n
                    \r\n \t
                  1. [latex]8a[\/latex]\r\n[reveal-answer q=\"658459\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"658459\"]8[\/hidden-answer]<\/li>\r\n \t
                  2. [latex]13m[\/latex]<\/li>\r\n \t
                  3. [latex]5{r}^{2}[\/latex]\r\n[reveal-answer q=\"495674\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"495674\"]5[\/hidden-answer]<\/li>\r\n \t
                  4. [latex]6{x}^{3}[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, identify all sets of like terms.\r\n
                      \r\n \t
                    1. [latex]{x}^{3},8x,14,8y,5,8{x}^{3}[\/latex]\r\n[reveal-answer q=\"104230\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"104230\"]x3, 8x3 and 14, 5[\/hidden-answer]<\/li>\r\n \t
                    2. [latex]6z,3{w}^{2},1,6{z}^{2},4z,{w}^{2}[\/latex]<\/li>\r\n \t
                    3. [latex]9a,{a}^{2},16ab,16{b}^{2},4ab,9{b}^{2}[\/latex]\r\n[reveal-answer q=\"243424\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"243424\"]16ab and 4ab; 16b2 and 9b2[\/hidden-answer]<\/li>\r\n \t
                    4. [latex]3,25{r}^{2},10s,10r,4{r}^{2},3s[\/latex]<\/li>\r\n<\/ol>\r\n

                      Simplify Expressions by Combining Like Terms<\/h3>\r\nIn the following exercises, simplify the given expression by combining like terms.\r\n
                        \r\n \t
                      1. [latex]10x+3x[\/latex]\r\n[reveal-answer q=\"702323\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"702323\"]13x[\/hidden-answer]<\/li>\r\n \t
                      2. [latex]15x+4x[\/latex]<\/li>\r\n \t
                      3. [latex]17a+9a[\/latex]\r\n[reveal-answer q=\"224148\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"224148\"]26a[\/hidden-answer]<\/li>\r\n \t
                      4. [latex]18z+9z[\/latex]<\/li>\r\n \t
                      5. [latex]4c+2c+c[\/latex]\r\n[reveal-answer q=\"764793\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"764793\"]7c[\/hidden-answer]<\/li>\r\n \t
                      6. [latex]6y+4y+y[\/latex]<\/li>\r\n \t
                      7. [latex]9x+3x+8[\/latex]\r\n[reveal-answer q=\"661888\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"661888\"]12x + 8[\/hidden-answer]<\/li>\r\n \t
                      8. [latex]8a+5a+9[\/latex]<\/li>\r\n \t
                      9. [latex]7u+2+3u+1[\/latex]\r\n[reveal-answer q=\"397131\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"397131\"]10u + 3[\/hidden-answer]<\/li>\r\n \t
                      10. [latex]8d+6+2d+5[\/latex]<\/li>\r\n \t
                      11. [latex]7p+6+5p+4[\/latex]\r\n[reveal-answer q=\"735329\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"735329\"]12p + 10[\/hidden-answer]<\/li>\r\n \t
                      12. [latex]8x+7+4x - 5[\/latex]<\/li>\r\n \t
                      13. [latex]10a+7+5a - 2+7a - 4[\/latex]\r\n[reveal-answer q=\"619827\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"619827\"]22a + 1[\/hidden-answer]<\/li>\r\n \t
                      14. [latex]7c+4+6c - 3+9c - 1[\/latex]<\/li>\r\n \t
                      15. [latex]3{x}^{2}+12x+11+14{x}^{2}+8x+5[\/latex]\r\n[reveal-answer q=\"741756\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"741756\"]17x2 + 20x + 16[\/hidden-answer]<\/li>\r\n \t
                      16. [latex]5{b}^{2}+9b+10+2{b}^{2}+3b - 4[\/latex]<\/li>\r\n<\/ol>\r\n

                        Translate English Phrases into Algebraic Expressions<\/h3>\r\nIn the following exercises, translate the given word phrase into an algebraic expression.\r\n
                          \r\n \t
                        1. The sum of 8 and 12\r\n[reveal-answer q=\"912721\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"912721\"]8 + 12[\/hidden-answer]<\/li>\r\n \t
                        2. The sum of 9 and 1<\/li>\r\n \t
                        3. The difference of 14 and 9\r\n[reveal-answer q=\"133191\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"133191\"]14 \u2212 9[\/hidden-answer]<\/li>\r\n \t
                        4. 8 less than 19<\/li>\r\n \t
                        5. The product of 9 and 7\r\n[reveal-answer q=\"428160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"428160\"]9 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                        6. The product of 8 and 7<\/li>\r\n \t
                        7. The quotient of 36 and 9\r\n[reveal-answer q=\"650756\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"650756\"]36 \u00f7 9[\/hidden-answer]<\/li>\r\n \t
                        8. The quotient of 42 and 7<\/li>\r\n \t
                        9. The difference of [latex]x[\/latex] and [latex]4[\/latex]\r\n[reveal-answer q=\"91575\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"91575\"]x \u2212 4[\/hidden-answer]<\/li>\r\n \t
                        10. [latex]3[\/latex] less than [latex]x[\/latex]<\/li>\r\n \t
                        11. The product of [latex]6[\/latex] and [latex]y[\/latex]\r\n[reveal-answer q=\"786240\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"786240\"]6y[\/hidden-answer]<\/li>\r\n \t
                        12. The product of [latex]9[\/latex] and [latex]y[\/latex]<\/li>\r\n \t
                        13. The sum of [latex]8x[\/latex] and [latex]3x[\/latex]\r\n[reveal-answer q=\"791593\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"791593\"]8x + 3x[\/hidden-answer]<\/li>\r\n \t
                        14. The sum of [latex]13x[\/latex] and [latex]3x[\/latex]<\/li>\r\n \t
                        15. The quotient of [latex]y[\/latex] and [latex]3[\/latex]\r\n[reveal-answer q=\"810173\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"810173\"][latex]\\Large\\frac{y}{3}[\/latex][\/hidden-answer]<\/li>\r\n \t
                        16. The quotient of [latex]y[\/latex] and [latex]8[\/latex]<\/li>\r\n \t
                        17. Eight times the difference of [latex]y[\/latex] and nine\r\n[reveal-answer q=\"365748\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"365748\"]8 (y \u2212 9)[\/hidden-answer]<\/li>\r\n \t
                        18. Seven times the difference of [latex]y[\/latex] and one<\/li>\r\n \t
                        19. Five times the sum of [latex]x[\/latex] and [latex]y[\/latex]\r\n[reveal-answer q=\"606543\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"606543\"]5 (x + y)[\/hidden-answer]<\/li>\r\n \t
                        20. Nine times five less than twice [latex]x[\/latex]<\/li>\r\n<\/ol>\r\n

                          Translate English Phrases into Algebraic Expressions<\/h3>\r\nIn the following exercises, write an algebraic expression.\r\n
                            \r\n \t
                          1. Adele bought a skirt and a blouse. The skirt cost [latex]\\$15[\/latex] more than the blouse. Let [latex]b[\/latex] represent the cost of the blouse. Write an expression for the cost of the skirt.\r\n[reveal-answer q=\"22951\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"22951\"]b + 15[\/hidden-answer]<\/li>\r\n \t
                          2. Eric has rock and classical CDs in his car. The number of rock CDs is [latex]3[\/latex] more than the number of classical CDs. Let [latex]c[\/latex] represent the number of classical CDs. Write an expression for the number of rock CDs.<\/li>\r\n \t
                          3. The number of girls in a second-grade class is [latex]4[\/latex] less than the number of boys. Let [latex]b[\/latex] represent the number of boys. Write an expression for the number of girls.\r\n[reveal-answer q=\"832666\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"832666\"]b \u2212 4[\/hidden-answer]<\/li>\r\n \t
                          4. Marcella has [latex]6[\/latex] fewer male cousins than female cousins. Let [latex]f[\/latex] represent the number of female cousins. Write an expression for the number of boy cousins.<\/li>\r\n \t
                          5. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let [latex]n[\/latex] represent the number of nickels. Write an expression for the number of pennies.\r\n[reveal-answer q=\"971786\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"971786\"]2n \u2212 7[\/hidden-answer]<\/li>\r\n \t
                          6. Jeannette has [latex]\\$5[\/latex] and [latex]\\$10[\/latex] bills in her wallet. The number of fives is three more than six times the number of tens. Let [latex]t[\/latex] represent the number of tens. Write an expression for the number of fives.<\/li>\r\n<\/ol>\r\n
                            \r\n

                            Everyday Math<\/h3>\r\nIn the following exercises, use algebraic expressions to solve the problem.\r\n

                            Car insurance<\/strong><\/h4>\r\nJustin\u2019s car insurance has a [latex]\\$750[\/latex] deductible per incident. This means that he pays [latex]\\$750[\/latex] and his insurance company will pay all costs beyond [latex]\\$750[\/latex]. If Justin files a claim for [latex]\\$2,100[\/latex], how much will he pay, and how much will his insurance company pay?\r\n\r\n[reveal-answer q=\"510916\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"510916\"]He will pay $750. His insurance company will pay $1350.[\/hidden-answer]\r\n

                            Home insurance<\/h4>\r\nPam and Armando\u2019s home insurance has a [latex]\\$2,500[\/latex] deductible per incident. This means that they pay [latex]\\$2,500[\/latex] and their insurance company will pay all costs beyond [latex]\\$2,500[\/latex]. If Pam and Armando file a claim for [latex]\\$19,400[\/latex], how much will they pay, and how much will their insurance company pay?\r\n\r\n<\/div>\r\n
                            \r\n

                            Writing Exercises<\/h3>\r\nExplain why \"the sum of x<\/em> and y<\/em>\" is the same as \"the sum of y<\/em> and x<\/em>,\" but \"the difference of x<\/em> and y<\/em>\" is not the same as \"the difference of y<\/em> and x<\/em>.\" Try substituting two random numbers for [latex]x[\/latex] and [latex]y[\/latex] to help you explain.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nExplain the difference between \"[latex]4[\/latex] times the sum of [latex]x[\/latex] and [latex]y[\/latex]\" and \"the sum of [latex]4[\/latex] times [latex]x[\/latex] and [latex]y[\/latex].\"\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                            Subtraction Property of Equality<\/h2>\r\n

                            Determine Whether a Number is a Solution of an Equation<\/h3>\r\nIn the following exercises, determine whether each given value is a solution to the equation.\r\n

                            Exercise 1<\/h4>\r\n[latex]x+13=21[\/latex]\r\n
                              \r\n \t
                            1. [latex]x=8[\/latex][reveal-answer q=\"389269\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"389269\"]yes[\/hidden-answer]<\/li>\r\n \t
                            2. [latex]x=34[\/latex][reveal-answer q=\"947842\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"947842\"]no[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                              Exercise 2<\/h4>\r\n[latex]y+18=25[\/latex]\r\n
                                \r\n \t
                              1. [latex]y=7[\/latex]<\/li>\r\n \t
                              2. [latex]y=43[\/latex]<\/li>\r\n<\/ol>\r\n

                                Exercise 3<\/h4>\r\n[latex]m - 4=13[\/latex]\r\n
                                  \r\n \t
                                1. [latex]m=9[\/latex][reveal-answer q=\"883575\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"883575\"]no[\/hidden-answer]<\/li>\r\n \t
                                2. [latex]m=17[\/latex][reveal-answer q=\"683469\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"683469\"]yes[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                  Exercise 4<\/h4>\r\n[latex]n - 9=6[\/latex]\r\n
                                    \r\n \t
                                  1. [latex]n=3[\/latex]<\/li>\r\n \t
                                  2. [latex]n=15[\/latex]<\/li>\r\n<\/ol>\r\n

                                    Exercise 5<\/h4>\r\n[latex]3p+6=15[\/latex]\r\n
                                      \r\n \t
                                    1. [latex]p=3[\/latex][reveal-answer q=\"644405\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"644405\"]yes[\/hidden-answer]<\/li>\r\n \t
                                    2. [latex]p=7[\/latex][reveal-answer q=\"765381\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"765381\"]no[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                      Exercise 6<\/h4>\r\n[latex]8q+4=20[\/latex]\r\n
                                        \r\n \t
                                      1. [latex]q=2[\/latex]<\/li>\r\n \t
                                      2. [latex]q=3[\/latex]<\/li>\r\n<\/ol>\r\n

                                        Exercise 7<\/h4>\r\n[latex]18d - 9=27[\/latex]\r\n
                                          \r\n \t
                                        1. [latex]d=1[\/latex][reveal-answer q=\"346023\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"346023\"]no[\/hidden-answer]<\/li>\r\n \t
                                        2. [latex]d=2[\/latex][reveal-answer q=\"583362\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"583362\"]yes[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                          Exercise 8<\/h4>\r\n[latex]24f - 12=60[\/latex]\r\n
                                            \r\n \t
                                          1. [latex]f=2[\/latex]<\/li>\r\n \t
                                          2. [latex]f=3[\/latex]<\/li>\r\n<\/ol>\r\n

                                            Exercise 9<\/h4>\r\n[latex]8u - 4=4u+40[\/latex]\r\n
                                              \r\n \t
                                            1. [latex]u=3[\/latex][reveal-answer q=\"302196\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"302196\"]no[\/hidden-answer]<\/li>\r\n \t
                                            2. [latex]u=11[\/latex][reveal-answer q=\"456014\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"456014\"]yes[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                              Exercise 10<\/h4>\r\n[latex]7v - 3=4v+36[\/latex]\r\n
                                                \r\n \t
                                              1. [latex]v=3[\/latex]<\/li>\r\n \t
                                              2. [latex]v=11[\/latex]<\/li>\r\n<\/ol>\r\n

                                                Exercise 11<\/h4>\r\n[latex]20h - 5=15h+35[\/latex]\r\n
                                                  \r\n \t
                                                1. [latex]h=6[\/latex][reveal-answer q=\"946435\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"946435\"]no[\/hidden-answer]<\/li>\r\n \t
                                                2. [latex]h=8[\/latex][reveal-answer q=\"954554\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"954554\"]yes[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                  Exercise 12<\/h4>\r\n[latex]18k - 3=12k+33[\/latex]\r\n
                                                    \r\n \t
                                                  1. [latex]k=1[\/latex]<\/li>\r\n \t
                                                  2. [latex]k=6[\/latex]<\/li>\r\n<\/ol>\r\n

                                                    Model the Subtraction Property of Equality<\/h3>\r\nIn the following exercises, write the equation modeled by the envelopes and counters and then solve using the subtraction property of equality.\r\n

                                                    Exercise 1<\/h4>\r\n\"The\r\n[reveal-answer q=\"861307\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"861307\"]x + 2 = 5; x = 3[\/hidden-answer]\r\n

                                                    Exercise 2<\/h4>\r\n\"The\r\n

                                                    Exercise 3<\/h4>\r\n\"The\r\n[reveal-answer q=\"818507\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"818507\"]x + 3 = 6; x = 3[\/hidden-answer]\r\n

                                                    Exercise 4<\/h4>\r\n\"The\r\n

                                                    Solve Equations using the Subtraction Property of Equality<\/h3>\r\nIn the following exercises, solve each equation using the subtraction property of equality.\r\n
                                                      \r\n \t
                                                    1. [latex]a+2=18[\/latex]\r\n[reveal-answer q=\"99320\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"99320\"]a<\/em> = 16[\/hidden-answer]<\/li>\r\n \t
                                                    2. [latex]b+5=13[\/latex]<\/li>\r\n \t
                                                    3. [latex]p+18=23[\/latex]\r\n[reveal-answer q=\"912195\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"912195\"]p<\/em> = 5[\/hidden-answer]<\/li>\r\n \t
                                                    4. [latex]q+14=31[\/latex]<\/li>\r\n \t
                                                    5. [latex]r+76=100[\/latex]\r\n[reveal-answer q=\"591632\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"591632\"]r<\/em> = 24[\/hidden-answer]<\/li>\r\n \t
                                                    6. [latex]s+62=95[\/latex]<\/li>\r\n \t
                                                    7. [latex]16=x+9[\/latex]\r\n[reveal-answer q=\"485168\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"485168\"]x<\/em> = 7[\/hidden-answer]<\/li>\r\n \t
                                                    8. [latex]17=y+6[\/latex]<\/li>\r\n \t
                                                    9. [latex]93=p+24[\/latex]\r\n[reveal-answer q=\"452230\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"452230\"]p<\/em> = 69[\/hidden-answer]<\/li>\r\n \t
                                                    10. [latex]116=q+79[\/latex]<\/li>\r\n \t
                                                    11. [latex]465=d+398[\/latex]\r\n[reveal-answer q=\"930520\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"930520\"]d<\/em> = 67[\/hidden-answer]<\/li>\r\n \t
                                                    12. [latex]932=c+641[\/latex]<\/li>\r\n<\/ol>\r\n

                                                      Solve Equations using the Addition Property of Equality<\/h3>\r\nIn the following exercises, solve each equation using the addition property of equality.\r\n
                                                        \r\n \t
                                                      1. [latex]y - 3=19[\/latex]\r\n[reveal-answer q=\"918010\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"918010\"]y<\/em> = 22[\/hidden-answer]<\/li>\r\n \t
                                                      2. [latex]x - 4=12[\/latex]<\/li>\r\n \t
                                                      3. [latex]u - 6=24[\/latex]\r\n[reveal-answer q=\"144963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"144963\"]u<\/em> = 30[\/hidden-answer]<\/li>\r\n \t
                                                      4. [latex]v - 7=35[\/latex]<\/li>\r\n \t
                                                      5. [latex]f - 55=123[\/latex]\r\n[reveal-answer q=\"725501\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"725501\"]f<\/em> = 178[\/hidden-answer]<\/li>\r\n \t
                                                      6. [latex]g - 39=117[\/latex]<\/li>\r\n \t
                                                      7. [latex]19=n - 13[\/latex]\r\n[reveal-answer q=\"981060\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"981060\"]n<\/em> = 32[\/hidden-answer]<\/li>\r\n \t
                                                      8. [latex]18=m - 15[\/latex]<\/li>\r\n \t
                                                      9. [latex]10=p - 38[\/latex]\r\n[reveal-answer q=\"665821\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"665821\"]p<\/em> = 48[\/hidden-answer]<\/li>\r\n \t
                                                      10. [latex]18=q - 72[\/latex]<\/li>\r\n \t
                                                      11. [latex]268=y - 199[\/latex]\r\n[reveal-answer q=\"57617\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"57617\"]y<\/em> = 467[\/hidden-answer]<\/li>\r\n \t
                                                      12. [latex]204=z - 149[\/latex]<\/li>\r\n<\/ol>\r\n

                                                        Translate Word Phrase to Algebraic Equations<\/h3>\r\nIn the following exercises, translate the given sentence into an algebraic equation.\r\n
                                                          \r\n \t
                                                        1. The sum of [latex]8[\/latex] and [latex]9[\/latex] is equal to [latex]17[\/latex].\r\n[reveal-answer q=\"782017\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"782017\"]8 + 9 = 17[\/hidden-answer]<\/li>\r\n \t
                                                        2. The sum of [latex]7[\/latex] and [latex]9[\/latex] is equal to [latex]16[\/latex].<\/li>\r\n \t
                                                        3. The difference of [latex]23[\/latex] and [latex]19[\/latex] is equal to [latex]4[\/latex].\r\n[reveal-answer q=\"156972\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"156972\"]23 \u2212 19 = 4[\/hidden-answer]<\/li>\r\n \t
                                                        4. The difference of [latex]29[\/latex] and [latex]12[\/latex] is equal to [latex]17[\/latex].<\/li>\r\n \t
                                                        5. The product of [latex]3[\/latex] and [latex]9[\/latex] is equal to [latex]27[\/latex].\r\n[reveal-answer q=\"167083\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"167083\"]3 \u22c5 9 = 27[\/hidden-answer]<\/li>\r\n \t
                                                        6. The product of [latex]6[\/latex] and [latex]8[\/latex] is equal to [latex]48[\/latex].<\/li>\r\n \t
                                                        7. The quotient of [latex]54[\/latex] and [latex]6[\/latex] is equal to [latex]9[\/latex].\r\n[reveal-answer q=\"554069\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"554069\"]54 \u00f7 6 = 9[\/hidden-answer]<\/li>\r\n \t
                                                        8. The quotient of [latex]42[\/latex] and [latex]7[\/latex] is equal to [latex]6[\/latex].<\/li>\r\n \t
                                                        9. Twice the difference of [latex]n[\/latex] and [latex]10[\/latex] gives [latex]52[\/latex].\r\n[reveal-answer q=\"900102\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"900102\"]2(n \u2212 10) = 52[\/hidden-answer]<\/li>\r\n \t
                                                        10. Twice the difference of [latex]m[\/latex] and [latex]14[\/latex] gives [latex]64[\/latex].<\/li>\r\n \t
                                                        11. The sum of three times [latex]y[\/latex] and [latex]10[\/latex] is [latex]100[\/latex].\r\n[reveal-answer q=\"228891\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"228891\"]3y<\/em> + 10 = 100[\/hidden-answer]<\/li>\r\n \t
                                                        12. The sum of eight times [latex]x[\/latex] and [latex]4[\/latex] is [latex]68[\/latex].<\/li>\r\n<\/ol>\r\n

                                                          Translate to an Equation and Solve<\/h3>\r\nIn the following exercises, translate the given sentence into an algebraic equation and then solve it.\r\n
                                                            \r\n \t
                                                          1. Five more than [latex]p[\/latex] is equal to [latex]21[\/latex].\r\n[reveal-answer q=\"255443\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"255443\"]p<\/em> + 5 = 21; p<\/em> = 16[\/hidden-answer]<\/li>\r\n \t
                                                          2. Nine more than [latex]q[\/latex] is equal to [latex]40[\/latex].<\/li>\r\n \t
                                                          3. The sum of [latex]r[\/latex] and [latex]18[\/latex] is [latex]73[\/latex].\r\n[reveal-answer q=\"486152\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"486152\"]r<\/em> + 18 = 73; r<\/em> = 55[\/hidden-answer]<\/li>\r\n \t
                                                          4. The sum of [latex]s[\/latex] and [latex]13[\/latex] is [latex]68[\/latex].<\/li>\r\n \t
                                                          5. The difference of [latex]d[\/latex] and [latex]30[\/latex] is equal to [latex]52[\/latex].\r\n[reveal-answer q=\"457783\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"457783\"]d<\/em> \u2212 30 = 52; d<\/em> = 82[\/hidden-answer]<\/li>\r\n \t
                                                          6. The difference of [latex]c[\/latex] and [latex]25[\/latex] is equal to [latex]75[\/latex].<\/li>\r\n \t
                                                          7. [latex]12[\/latex] less than [latex]u[\/latex] is [latex]89[\/latex].\r\n[reveal-answer q=\"739781\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"739781\"]u<\/em> \u2212 12 = 89; u<\/em> = 101[\/hidden-answer]<\/li>\r\n \t
                                                          8. [latex]19[\/latex] less than [latex]w[\/latex] is [latex]56[\/latex].<\/li>\r\n \t
                                                          9. [latex]325[\/latex] less than [latex]c[\/latex] gives [latex]799[\/latex].\r\n[reveal-answer q=\"274017\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"274017\"]c<\/em> \u2212 325 = 799; c<\/em> = 1124[\/hidden-answer]<\/li>\r\n \t
                                                          10. [latex]299[\/latex] less than [latex]d[\/latex] gives [latex]850[\/latex].<\/li>\r\n<\/ol>\r\n
                                                            \r\n

                                                            Everyday Math<\/h3>\r\n

                                                            Insurance<\/h4>\r\nVince\u2019s car insurance has a [latex]\\$500[\/latex] deductible. Find the amount the insurance company will pay, [latex]p[\/latex], for an [latex]\\$1800[\/latex] claim by solving the equation [latex]500+p=1800[\/latex].\r\n\r\n[reveal-answer q=\"455054\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"455054\"]$1300[\/hidden-answer]\r\n

                                                            Insurance<\/h4>\r\nMarta\u2019s homeowner\u2019s insurance policy has a [latex]\\$750[\/latex] deductible. The insurance company paid [latex]\\$5800[\/latex] to repair damages caused by a storm. Find the total cost of the storm damage, [latex]d[\/latex], by solving the equation [latex]d - 750=5800[\/latex].\r\n

                                                            Sale purchase<\/h4>\r\nArthur bought a suit that was on sale for [latex]\\$120[\/latex] off. He paid [latex]\\$340[\/latex] for the suit. Find the original price, [latex]p[\/latex], of the suit by solving the equation [latex]p - 120=340[\/latex].\r\n\r\n[reveal-answer q=\"368441\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"368441\"]$460[\/hidden-answer]\r\n

                                                            Sale purchase<\/h4>\r\nRita bought a sofa that was on sale for [latex]\\$1299[\/latex]. She paid a total of [latex]\\$1409[\/latex], including sales tax. Find the amount of the sales tax, [latex]t[\/latex], by solving the equation [latex]1299+t=1409[\/latex].\r\n\r\n<\/div>\r\n
                                                            \r\n

                                                            Writing Exercises<\/h3>\r\nIs [latex]x=1[\/latex] a solution to the equation [latex]8x - 2=16 - 6x?[\/latex] How do you know?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nWrite the equation [latex]y - 5=21[\/latex] in words. Then make up a word problem for this equation.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n
                                                            \r\n

                                                            Finding Multiples and Factors<\/h2>\r\n

                                                            Identify Multiples of Numbers<\/strong><\/h3>\r\n

                                                            In the following exercises, list all the multiples less than [latex]50[\/latex] for the given number.<\/p>\r\n\r\n

                                                            \r\n
                                                            \r\n
                                                              \r\n \t
                                                            1. [latex]2[\/latex]\r\n[reveal-answer q=\"747955\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"747955\"]2, 4, 6, 8, 10 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48[\/hidden-answer]<\/li>\r\n \t
                                                            2. [latex]3[\/latex]<\/li>\r\n \t
                                                            3. [latex]4[\/latex]\r\n[reveal-answer q=\"452619\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"452619\"]4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48[\/hidden-answer]<\/li>\r\n \t
                                                            4. [latex]5[\/latex]<\/li>\r\n \t
                                                            5. [latex]6[\/latex]\r\n[reveal-answer q=\"670423\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"670423\"]6, 12, 18, 24, 30, 36, 42, 48[\/hidden-answer]<\/li>\r\n \t
                                                            6. [latex]7[\/latex]<\/li>\r\n \t
                                                            7. [latex]8[\/latex]\r\n[reveal-answer q=\"228723\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"228723\"]8, 16, 24, 32, 40, 48[\/hidden-answer]<\/li>\r\n \t
                                                            8. [latex]9[\/latex]<\/li>\r\n \t
                                                            9. [latex]10[\/latex]\r\n[reveal-answer q=\"58167\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"58167\"]10, 20, 30, 40[\/hidden-answer]<\/li>\r\n \t
                                                            10. [latex]12[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                              Use Common Divisibility Tests<\/h3>\r\n

                                                              In the following exercises, use the divisibility tests to determine whether each number is divisible by [latex]2,3,4,5,6,\\text{and}10[\/latex].<\/p>\r\n\r\n

                                                              \r\n
                                                              \r\n
                                                                \r\n \t
                                                              1. [latex]84[\/latex]\r\n[reveal-answer q=\"278301\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"278301\"]Divisible by 2, 3, 4, 6[\/hidden-answer]<\/li>\r\n \t
                                                              2. [latex]96[\/latex]<\/li>\r\n \t
                                                              3. [latex]75[\/latex]\r\n[reveal-answer q=\"652071\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"652071\"]Divisible by 3, 5[\/hidden-answer]<\/li>\r\n \t
                                                              4. [latex]78[\/latex]<\/li>\r\n \t
                                                              5. [latex]168[\/latex]\r\n[reveal-answer q=\"88945\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"88945\"]Divisible by 2, 3, 4, 6[\/hidden-answer]<\/li>\r\n \t
                                                              6. [latex]264[\/latex]<\/li>\r\n \t
                                                              7. [latex]900[\/latex]\r\n[reveal-answer q=\"184448\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"184448\"]Divisible by 2, 3, 4, 5, 6, 10[\/hidden-answer]<\/li>\r\n \t
                                                              8. [latex]800[\/latex]<\/li>\r\n \t
                                                              9. [latex]896[\/latex]\r\n[reveal-answer q=\"407857\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"407857\"]Divisible by 2, 4[\/hidden-answer]<\/li>\r\n \t
                                                              10. [latex]942[\/latex]<\/li>\r\n \t
                                                              11. [latex]375[\/latex]\r\n[reveal-answer q=\"762698\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"762698\"]Divisible by 3, 5[\/hidden-answer]<\/li>\r\n \t
                                                              12. [latex]750[\/latex]<\/li>\r\n \t
                                                              13. [latex]350[\/latex]\r\n[reveal-answer q=\"906106\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"906106\"]Divisible by 2, 5, 10[\/hidden-answer]<\/li>\r\n \t
                                                              14. [latex]550[\/latex]<\/li>\r\n \t
                                                              15. [latex]1430[\/latex]\r\n[reveal-answer q=\"392275\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"392275\"]Divisible by 2, 5, 10[\/hidden-answer]<\/li>\r\n \t
                                                              16. [latex]1080[\/latex]<\/li>\r\n \t
                                                              17. [latex]22,335[\/latex]\r\n[reveal-answer q=\"586170\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"586170\"]Divisible by 3, 5[\/hidden-answer]<\/li>\r\n \t
                                                              18. [latex]39,075[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                Find All the Factors of a Number<\/h3>\r\n

                                                                In the following exercises, find all the factors of the given number.<\/p>\r\n\r\n

                                                                \r\n
                                                                \r\n
                                                                  \r\n \t
                                                                1. [latex]36[\/latex]\r\n[reveal-answer q=\"889572\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"889572\"]1, 2, 3, 4, 6, 9, 12, 18, 36[\/hidden-answer]<\/li>\r\n \t
                                                                2. [latex]42[\/latex]<\/li>\r\n \t
                                                                3. [latex]60[\/latex]\r\n[reveal-answer q=\"703215\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"703215\"]1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60[\/hidden-answer]<\/li>\r\n \t
                                                                4. [latex]48[\/latex]<\/li>\r\n \t
                                                                5. [latex]144[\/latex]\r\n[reveal-answer q=\"410767\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"410767\"]1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 48, 72,144[\/hidden-answer]<\/li>\r\n \t
                                                                6. [latex]200[\/latex]<\/li>\r\n \t
                                                                7. [latex]588[\/latex]\r\n[reveal-answer q=\"948186\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"948186\"]1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588[\/hidden-answer]<\/li>\r\n \t
                                                                8. [latex]576[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                  Identify Prime and Composite Numbers<\/h3>\r\n

                                                                  In the following exercises, determine if the given number is prime or composite.<\/p>\r\n\r\n

                                                                  \r\n
                                                                  \r\n
                                                                    \r\n \t
                                                                  1. [latex]43[\/latex]\r\n[reveal-answer q=\"246407\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"246407\"]prime[\/hidden-answer]<\/li>\r\n \t
                                                                  2. [latex]67[\/latex]<\/li>\r\n \t
                                                                  3. [latex]39[\/latex]\r\n[reveal-answer q=\"331457\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"331457\"]composite[\/hidden-answer]<\/li>\r\n \t
                                                                  4. [latex]53[\/latex]<\/li>\r\n \t
                                                                  5. [latex]71[\/latex]\r\n[reveal-answer q=\"320699\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"320699\"]prime[\/hidden-answer]<\/li>\r\n \t
                                                                  6. [latex]119[\/latex]<\/li>\r\n \t
                                                                  7. [latex]481[\/latex]\r\n[reveal-answer q=\"269740\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"269740\"]composite[\/hidden-answer]<\/li>\r\n \t
                                                                  8. [latex]221[\/latex]<\/li>\r\n \t
                                                                  9. [latex]209[\/latex]\r\n[reveal-answer q=\"498783\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"498783\"]composite[\/hidden-answer]<\/li>\r\n \t
                                                                  10. [latex]359[\/latex]<\/li>\r\n \t
                                                                  11. [latex]667[\/latex]\r\n[reveal-answer q=\"537601\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"537601\"]composite[\/hidden-answer]<\/li>\r\n \t
                                                                  12. [latex]1771[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                    \r\n
                                                                    \r\n

                                                                    Everyday Math<\/h3>\r\n
                                                                    \r\n
                                                                    \r\n

                                                                    Banking<\/h4>\r\nFrank\u2019s grandmother gave him [latex]\\$100[\/latex] at his high school graduation. Instead of spending it, Frank opened a bank account. Every week, he added [latex]\\$15[\/latex] to the account. The table shows how much money Frank had put in the account by the end of each week. Complete the table by filling in the blanks.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                                                                    Weeks after graduation<\/strong><\/th>\r\nTotal number of dollars Frank put in the account<\/strong><\/th>\r\nSimplified Total<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                                                                    [latex]0[\/latex]<\/td>\r\n[latex]100[\/latex]<\/td>\r\n[latex]100[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]1[\/latex]<\/td>\r\n[latex]100+15[\/latex]<\/td>\r\n[latex]115[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]2[\/latex]<\/td>\r\n[latex]100+15\\cdot 2[\/latex]<\/td>\r\n[latex]130[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]3[\/latex]<\/td>\r\n[latex]100+15\\cdot 3[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]4[\/latex]<\/td>\r\n[latex]100+15\\cdot \\left[\\right][\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]5[\/latex]<\/td>\r\n[latex]100+\\left[\\right][\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]6[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]20[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]x[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
                                                                    \r\n
                                                                    [reveal-answer q=\"312493\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"312493\"]\"This<\/span>[\/hidden-answer]<\/div>\r\n<\/div>\r\n<\/div>\r\n
                                                                    \r\n
                                                                    \r\n

                                                                    Banking<\/h4>\r\nIn March, Gina opened a Christmas club savings account at her bank. She deposited [latex]\\$75[\/latex] to open the account. Every week, she added [latex]\\$20[\/latex] to the account. The table shows how much money Gina had put in the account by the end of each week. Complete the table by filling in the blanks.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                                                                    Weeks after opening the account<\/strong><\/th>\r\nTotal number of dollars Gina put in the account<\/strong><\/th>\r\nSimplified Total<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n
                                                                    [latex]0[\/latex]<\/td>\r\n[latex]75[\/latex]<\/td>\r\n[latex]75[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]1[\/latex]<\/td>\r\n[latex]75+20[\/latex]<\/td>\r\n[latex]95[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]2[\/latex]<\/td>\r\n[latex]75+20\\cdot 2[\/latex]<\/td>\r\n[latex]115[\/latex]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]3[\/latex]<\/td>\r\n[latex]75+20\\cdot 3[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]4[\/latex]<\/td>\r\n[latex]75+20\\cdot \\left[\\right][\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]5[\/latex]<\/td>\r\n[latex]75+\\left[\\right][\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]6[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]20[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n
                                                                    [latex]x[\/latex]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n[practice-area rows=\"1\"][\/practice-area]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                    \r\n
                                                                    \r\n

                                                                    Writing Exercises<\/h3>\r\n
                                                                    \r\n
                                                                    \r\n\r\nIf a number is divisible by [latex]2[\/latex] and by [latex]3[\/latex], why is it also divisible by [latex]6?[\/latex]\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nWhat is the difference between prime numbers and composite numbers?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                    <\/section><\/section>
                                                                    \r\n

                                                                    Prime Factorization and the Least Common Multiple<\/h2>\r\n

                                                                    Find the Prime Factorization of a Composite Number<\/strong><\/h3>\r\n

                                                                    In the following exercises, find the prime factorization of each number using the factor tree method.<\/p>\r\n\r\n

                                                                    \r\n
                                                                    \r\n
                                                                      \r\n \t
                                                                    1. [latex]86[\/latex]\r\n[reveal-answer q=\"889607\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"889607\"]2 \u22c5 43[\/hidden-answer]<\/li>\r\n \t
                                                                    2. [latex]78[\/latex]<\/li>\r\n \t
                                                                    3. [latex]132[\/latex]\r\n[reveal-answer q=\"955964\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"955964\"]2 \u22c5 2 \u22c5 3 \u22c5 11[\/hidden-answer]<\/li>\r\n \t
                                                                    4. [latex]455[\/latex]<\/li>\r\n \t
                                                                    5. [latex]693[\/latex]\r\n[reveal-answer q=\"136778\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"136778\"]3 \u22c5 3 \u22c5 7 \u22c5 11[\/hidden-answer]<\/li>\r\n \t
                                                                    6. [latex]420[\/latex]<\/li>\r\n \t
                                                                    7. [latex]115[\/latex]\r\n[reveal-answer q=\"24769\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"24769\"]5 \u22c5 23[\/hidden-answer]<\/li>\r\n \t
                                                                    8. [latex]225[\/latex]<\/li>\r\n \t
                                                                    9. [latex]2475[\/latex]\r\n[reveal-answer q=\"376393\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"376393\"]3 \u22c5 3 \u22c5 5 \u22c5 5 \u22c5 11[\/hidden-answer]<\/li>\r\n \t
                                                                    10. 1560<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                      Find the Prime Factorization of a Composite Number<\/strong><\/h3>\r\n

                                                                      In the following exercises, find the prime factorization of each number using the ladder method.<\/p>\r\n\r\n

                                                                      \r\n
                                                                      \r\n
                                                                        \r\n \t
                                                                      1. [latex]56[\/latex]\r\n[reveal-answer q=\"920793\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920793\"]2 \u22c5 2 \u22c5 2 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                      2. [latex]72[\/latex]<\/li>\r\n \t
                                                                      3. [latex]168[\/latex]\r\n[reveal-answer q=\"715677\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"715677\"]2 \u22c5 2 \u22c5 2 \u22c5 3 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                      4. [latex]252[\/latex]<\/li>\r\n \t
                                                                      5. [latex]391[\/latex]\r\n[reveal-answer q=\"360613\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"360613\"]17 \u22c5 23[\/hidden-answer]<\/li>\r\n \t
                                                                      6. [latex]400[\/latex]<\/li>\r\n \t
                                                                      7. [latex]432[\/latex]\r\n[reveal-answer q=\"320583\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"320583\"]2 \u22c5 2 \u22c5 2 \u22c5 2 \u22c5 3 \u22c5 3 \u22c5 3[\/hidden-answer]<\/li>\r\n \t
                                                                      8. [latex]627[\/latex]<\/li>\r\n \t
                                                                      9. [latex]2160[\/latex]\r\n[reveal-answer q=\"770615\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"770615\"]2 \u22c5 2 \u22c5 2 \u22c5 2 \u22c5 3 \u22c5 3 \u22c5 3 \u22c5 5[\/hidden-answer]<\/li>\r\n \t
                                                                      10. [latex]2520[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                        Find the Prime Factorization of a Composite Number<\/strong><\/h3>\r\n

                                                                        In the following exercises, find the prime factorization of each number using any method.<\/p>\r\n\r\n

                                                                        \r\n
                                                                        \r\n
                                                                          \r\n \t
                                                                        1. [latex]150[\/latex]\r\n[reveal-answer q=\"641945\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"641945\"]2 \u22c5 3 \u22c5 5 \u22c5 5[\/hidden-answer]<\/li>\r\n \t
                                                                        2. [latex]180[\/latex]<\/li>\r\n \t
                                                                        3. [latex]525[\/latex]\r\n[reveal-answer q=\"148477\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"148477\"]3 \u22c5 5 \u22c5 5 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                        4. [latex]444[\/latex]<\/li>\r\n \t
                                                                        5. [latex]36[\/latex]\r\n[reveal-answer q=\"349306\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"349306\"]2 \u22c5 2 \u22c5 3 \u22c5 3[\/hidden-answer]<\/li>\r\n \t
                                                                        6. [latex]50[\/latex]<\/li>\r\n \t
                                                                        7. [latex]350[\/latex]\r\n[reveal-answer q=\"660759\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"660759\"]2 \u22c5 5 \u22c5 5 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                        8. [latex]144[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                          Find the Least Common Multiple (LCM) of Two Numbers<\/strong><\/h3>\r\nIn the following exercises, find the least common multiple (LCM) by listing multiples.\r\n
                                                                          \r\n
                                                                          \r\n
                                                                            \r\n \t
                                                                          1. [latex]8,12[\/latex]\r\n[reveal-answer q=\"973164\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"973164\"]24[\/hidden-answer]<\/li>\r\n \t
                                                                          2. [latex]4,3[\/latex]<\/li>\r\n \t
                                                                          3. [latex]6,15[\/latex]\r\n[reveal-answer q=\"920363\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920363\"]30[\/hidden-answer]<\/li>\r\n \t
                                                                          4. [latex]12,16[\/latex]<\/li>\r\n \t
                                                                          5. [latex]30,40[\/latex]\r\n[reveal-answer q=\"381033\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"381033\"]120[\/hidden-answer]<\/li>\r\n \t
                                                                          6. [latex]20,30[\/latex]<\/li>\r\n \t
                                                                          7. [latex]60,75[\/latex]\r\n[reveal-answer q=\"140539\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"140539\"]300[\/hidden-answer]<\/li>\r\n \t
                                                                          8. [latex]44,55[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                            Find the Least Common Multiple (LCM) of Two Numbers<\/strong><\/h3>\r\n

                                                                            In the following exercises, find the least common multiple (LCM) by using the prime factors method.<\/p>\r\n\r\n

                                                                            \r\n
                                                                            \r\n
                                                                              \r\n \t
                                                                            1. [latex]8,12[\/latex]\r\n[reveal-answer q=\"342736\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"342736\"]24[\/hidden-answer]<\/li>\r\n \t
                                                                            2. [latex]12,16[\/latex]<\/li>\r\n \t
                                                                            3. [latex]24,30[\/latex]\r\n[reveal-answer q=\"754616\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"754616\"]120[\/hidden-answer]<\/li>\r\n \t
                                                                            4. [latex]28,40[\/latex]<\/li>\r\n \t
                                                                            5. [latex]70,84[\/latex]\r\n[reveal-answer q=\"341877\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"341877\"]420[\/hidden-answer]<\/li>\r\n \t
                                                                            6. [latex]84,90[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

                                                                              Find the Least Common Multiple (LCM) of Two Numbers<\/strong><\/h3>\r\n

                                                                              In the following exercises, find the least common multiple (LCM) using any method.<\/p>\r\n\r\n

                                                                              \r\n
                                                                              \r\n
                                                                                \r\n \t
                                                                              1. [latex]6,21[\/latex]\r\n[reveal-answer q=\"307419\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"307419\"]42[\/hidden-answer]<\/li>\r\n \t
                                                                              2. [latex]9,15[\/latex]<\/li>\r\n \t
                                                                              3. [latex]24,30[\/latex]\r\n[reveal-answer q=\"396620\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"396620\"]120[\/hidden-answer]<\/li>\r\n \t
                                                                              4. [latex]32,40[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                                \r\n
                                                                                \r\n

                                                                                Everyday Math<\/h3>\r\n
                                                                                \r\n
                                                                                \r\n

                                                                                Grocery shopping<\/h4>\r\nHot dogs are sold in packages of ten, but hot dog buns come in packs of eight. What is the smallest number of hot dogs and buns that can be purchased if you want to have the same number of hot dogs and buns? (Hint: it is the LCM!)\r\n[reveal-answer q=\"657697\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"657697\"]40[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n
                                                                                \r\n
                                                                                \r\n

                                                                                Grocery shopping<\/h4>\r\nPaper plates are sold in packages of [latex]12[\/latex] and party cups come in packs of [latex]8[\/latex]. What is the smallest number of plates and cups you can purchase if you want to have the same number of each? (Hint: it is the LCM!)\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                                \r\n
                                                                                \r\n

                                                                                Writing Exercises<\/h3>\r\n
                                                                                \r\n
                                                                                \r\n\r\nDo you prefer to find the prime factorization of a composite number by using the factor tree method or the ladder method? Why?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nDo you prefer to find the LCM by listing multiples or by using the prime factors method? Why?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>
                                                                                <\/section><\/section>
                                                                                <\/section>\r\n

                                                                                Chapter Review Exercises<\/h2>\r\n
                                                                                \r\n

                                                                                Use the Language of Algebra<\/h3>\r\n

                                                                                Use Variables and Algebraic Symbols<\/h4>\r\nIn the following exercises, translate from algebra to English.\r\n
                                                                                  \r\n \t
                                                                                1. [latex]3\\cdot 8[\/latex]\r\n[reveal-answer q=\"908325\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"908325\"]the product of 3 and 8[\/hidden-answer]<\/li>\r\n \t
                                                                                2. [latex]12-x[\/latex]<\/li>\r\n \t
                                                                                3. [latex]24\\div 6[\/latex]\r\n[reveal-answer q=\"743113\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"743113\"]the quotient of 24 and 6[\/hidden-answer]<\/li>\r\n \t
                                                                                4. [latex]9+2a[\/latex]<\/li>\r\n \t
                                                                                5. [latex]50\\ge 47[\/latex]\r\n[reveal-answer q=\"912106\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"912106\"]50 is greater than or equal to 47[\/hidden-answer]<\/li>\r\n \t
                                                                                6. [latex]3y<15[\/latex]<\/li>\r\n \t
                                                                                7. [latex]n+4=13[\/latex]\r\n[reveal-answer q=\"553696\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"553696\"]The sum of n and 4 is equal to 13[\/hidden-answer]<\/li>\r\n \t
                                                                                8. [latex]32-k=7[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                  Identify Expressions and Equations<\/h4>\r\nIn the following exercises, determine if each is an expression or equation.\r\n
                                                                                    \r\n \t
                                                                                  1. [latex]5+u=84[\/latex]\r\n[reveal-answer q=\"124381\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"124381\"]equation[\/hidden-answer]<\/li>\r\n \t
                                                                                  2. [latex]36 - 6s[\/latex]<\/li>\r\n \t
                                                                                  3. [latex]4y - 11[\/latex]\r\n[reveal-answer q=\"367521\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"367521\"]expression[\/hidden-answer]<\/li>\r\n \t
                                                                                  4. [latex]10x=120[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                    Simplify Expressions with Exponents<\/h4>\r\nIn the following exercises, write in exponential form.\r\n
                                                                                      \r\n \t
                                                                                    1. [latex]2\\cdot 2\\cdot 2[\/latex]\r\n[reveal-answer q=\"372392\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"372392\"]23<\/sup>[\/hidden-answer]<\/li>\r\n \t
                                                                                    2. [latex]a\\cdot a\\cdot a\\cdot a\\cdot a[\/latex]<\/li>\r\n \t
                                                                                    3. [latex]x\\cdot x\\cdot x\\cdot x\\cdot x\\cdot x[\/latex]\r\n[reveal-answer q=\"318881\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"318881\"]x6<\/sup>[\/hidden-answer]<\/li>\r\n \t
                                                                                    4. [latex]10\\cdot 10\\cdot 10[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                      Simplify Expressions with Exponents<\/h4>\r\nIn the following exercises, write in expanded form.\r\n
                                                                                        \r\n \t
                                                                                      1. [latex]{8}^{4}[\/latex]\r\n[reveal-answer q=\"464335\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"464335\"]8 \u22c5 8 \u22c5 8 \u22c5 8[\/hidden-answer]<\/li>\r\n \t
                                                                                      2. [latex]{3}^{6}[\/latex]<\/li>\r\n \t
                                                                                      3. [latex]{y}^{5}[\/latex]\r\n[reveal-answer q=\"135513\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"135513\"]y \u22c5 y \u22c5 y \u22c5 y \u22c5 y[\/hidden-answer]<\/li>\r\n \t
                                                                                      4. [latex]{n}^{4}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                        Simplify Expressions with Exponents<\/h4>\r\nIn the following exercises, simplify each expression.\r\n
                                                                                          \r\n \t
                                                                                        1. [latex]{3}^{4}[\/latex]\r\n[reveal-answer q=\"624934\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"624934\"]81[\/hidden-answer]<\/li>\r\n \t
                                                                                        2. [latex]{10}^{6}[\/latex]<\/li>\r\n \t
                                                                                        3. [latex]{2}^{7}[\/latex]\r\n[reveal-answer q=\"752955\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"752955\"]128[\/hidden-answer]<\/li>\r\n \t
                                                                                        4. [latex]{4}^{3}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                          Simplify Expressions Using the Order of Operations<\/h4>\r\nIn the following exercises, simplify.\r\n
                                                                                            \r\n \t
                                                                                          1. [latex]10+2\\cdot 5[\/latex]\r\n[reveal-answer q=\"665669\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"665669\"]20[\/hidden-answer]<\/li>\r\n \t
                                                                                          2. [latex]\\left(10+2\\right)\\cdot 5[\/latex]<\/li>\r\n \t
                                                                                          3. [latex]\\left(30+6\\right)\\div 2[\/latex]\r\n[reveal-answer q=\"930419\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"930419\"]18[\/hidden-answer]<\/li>\r\n \t
                                                                                          4. [latex]30+6\\div 2[\/latex]<\/li>\r\n \t
                                                                                          5. [latex]{7}^{2}+{5}^{2}[\/latex]\r\n[reveal-answer q=\"868899\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"868899\"]74[\/hidden-answer]<\/li>\r\n \t
                                                                                          6. [latex]{\\left(7+5\\right)}^{2}[\/latex]<\/li>\r\n \t
                                                                                          7. [latex]4+3\\left(10 - 1\\right)[\/latex]\r\n[reveal-answer q=\"914077\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"914077\"]31[\/hidden-answer]<\/li>\r\n \t
                                                                                          8. [latex]\\left(4+3\\right)\\left(10 - 1\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                            \r\n

                                                                                            Evaluate, Simplify, and Translate Expressions<\/h3>\r\n

                                                                                            Evaluate an Expression<\/h4>\r\nIn the following exercises, evaluate the following expressions.\r\n
                                                                                              \r\n \t
                                                                                            1. [latex]9x - 5\\text{ when }x=7[\/latex]\r\n[reveal-answer q=\"618282\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"618282\"]58[\/hidden-answer]<\/li>\r\n \t
                                                                                            2. [latex]{y}^{3}\\text{ when }y=5[\/latex]<\/li>\r\n \t
                                                                                            3. [latex]3a - 4b[\/latex] when [latex]a=10,b=1[\/latex]\r\n[reveal-answer q=\"289628\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"289628\"]26[\/hidden-answer]<\/li>\r\n \t
                                                                                            4. [latex]bh\\text{ when }b=7,h=8[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                              Identify Terms, Coefficients and Like Terms<\/h4>\r\nIn the following exercises, identify the terms in each expression.\r\n
                                                                                                \r\n \t
                                                                                              1. [latex]12{n}^{2}+3n+1[\/latex]\r\n[reveal-answer q=\"205776\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"205776\"]12n2,3n, 1[\/hidden-answer]<\/li>\r\n \t
                                                                                              2. [latex]4{x}^{3}+11x+3[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                Identify Terms, Coefficients and Like Terms<\/h4>\r\nIn the following exercises, identify the coefficient of each term.\r\n
                                                                                                  \r\n \t
                                                                                                1. [latex]6y[\/latex]\r\n[reveal-answer q=\"723276\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"723276\"]6[\/hidden-answer]<\/li>\r\n \t
                                                                                                2. [latex]13{x}^{2}[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, identify the like terms.\r\n
                                                                                                    \r\n \t
                                                                                                  1. [latex]5{x}^{2},3,5{y}^{2},3x,x,4[\/latex]\r\n[reveal-answer q=\"964982\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"964982\"]3, 4, and 3x, x[\/hidden-answer]<\/li>\r\n \t
                                                                                                  2. [latex]8,8{r}^{2},\\text{8}r,3r,{r}^{2},3s[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                    Simplify Expressions by Combining Like Terms<\/h4>\r\nIn the following exercises, simplify the following expressions by combining like terms.\r\n
                                                                                                      \r\n \t
                                                                                                    1. [latex]15a+9a[\/latex]\r\n[reveal-answer q=\"47925\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"47925\"]24a[\/hidden-answer]<\/li>\r\n \t
                                                                                                    2. [latex]12y+3y+y[\/latex]<\/li>\r\n \t
                                                                                                    3. [latex]4x+7x+3x[\/latex]\r\n[reveal-answer q=\"327200\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"327200\"]14x[\/hidden-answer]<\/li>\r\n \t
                                                                                                    4. [latex]6+5c+3[\/latex]<\/li>\r\n \t
                                                                                                    5. [latex]8n+2+4n+9[\/latex]\r\n[reveal-answer q=\"394484\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"394484\"]12n + 11[\/hidden-answer]<\/li>\r\n \t
                                                                                                    6. [latex]19p+5+4p - 1+3p[\/latex]<\/li>\r\n \t
                                                                                                    7. [latex]7{y}^{2}+2y+11+3{y}^{2}-8[\/latex]\r\n[reveal-answer q=\"839094\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"839094\"]10y2 + 2y + 3[\/hidden-answer]<\/li>\r\n \t
                                                                                                    8. [latex]13{x}^{2}-x+6+5{x}^{2}+9x[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                      Translate English Phrases to Algebraic Expressions<\/h4>\r\nIn the following exercises, translate the following phrases into algebraic expressions.\r\n
                                                                                                        \r\n \t
                                                                                                      1. the difference of [latex]x[\/latex] and [latex]6[\/latex]\r\n[reveal-answer q=\"372980\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"372980\"]x \u2212 6[\/hidden-answer]<\/li>\r\n \t
                                                                                                      2. the sum of [latex]10[\/latex] and twice [latex]a[\/latex]<\/li>\r\n \t
                                                                                                      3. the product of [latex]3n[\/latex] and [latex]9[\/latex]\r\n[reveal-answer q=\"829752\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"829752\"]3n \u22c5 9[\/hidden-answer]<\/li>\r\n \t
                                                                                                      4. the quotient of [latex]s[\/latex] and [latex]4[\/latex]<\/li>\r\n \t
                                                                                                      5. [latex]5[\/latex] times the sum of [latex]y[\/latex] and [latex]1[\/latex]\r\n[reveal-answer q=\"173948\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"173948\"]5(y + 1)[\/hidden-answer]<\/li>\r\n \t
                                                                                                      6. [latex]10[\/latex] less than the product of [latex]5[\/latex] and [latex]z[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                        Translate English Phrases to Algebraic Expressions<\/h4>\r\nIn the following exercises, write the algebraic expressions that can be found in each sentence.\r\n
                                                                                                          \r\n \t
                                                                                                        1. Jack bought a sandwich and a coffee. The cost of the sandwich was [latex]\\$3[\/latex] more than the cost of the coffee. Call the cost of the coffee [latex]c[\/latex]. Write an expression for the cost of the sandwich.\r\n[reveal-answer q=\"236565\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"236565\"]c + 3[\/hidden-answer]<\/li>\r\n \t
                                                                                                        2. The number of poetry books on Brianna\u2019s bookshelf is [latex]5[\/latex] less than twice the number of novels. Call the number of novels [latex]n[\/latex]. Write an expression for the number of poetry books.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                          \r\n

                                                                                                          Subtraction Property of Equality<\/h3>\r\n

                                                                                                          Determine Whether a Number is a Solution of an Equation<\/h4>\r\nIn the following exercises, determine whether each number is a solution to the equation.\r\n

                                                                                                          Exercise 1<\/h5>\r\n[latex]y+16=40[\/latex]\r\n
                                                                                                            \r\n \t
                                                                                                          1. [latex]24[\/latex]\r\n[reveal-answer q=\"284039\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"284039\"]yes[\/hidden-answer]<\/li>\r\n \t
                                                                                                          2. [latex]56[\/latex]\r\n[reveal-answer q=\"83130\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"83130\"]no[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                            Exercise 2<\/h5>\r\n[latex]d - 6=21[\/latex]\r\n
                                                                                                              \r\n \t
                                                                                                            1. \u00a0[latex]15[\/latex]<\/li>\r\n \t
                                                                                                            2. [latex]27[\/latex]<\/li>\r\n<\/ol>\r\n
                                                                                                              Exercise 3<\/h5>\r\n[latex]4n+12=36[\/latex]\r\n
                                                                                                                \r\n \t
                                                                                                              1. [latex]6[\/latex]\r\n[reveal-answer q=\"783659\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"783659\"]yes[\/hidden-answer]<\/li>\r\n \t
                                                                                                              2. [latex]12[\/latex]\r\n[reveal-answer q=\"944016\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"944016\"]No[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                                Exercise 4<\/h5>\r\n[latex]20q - 10=70[\/latex]\r\n
                                                                                                                  \r\n \t
                                                                                                                1. [latex]3[\/latex]<\/li>\r\n \t
                                                                                                                2. [latex]4[\/latex]<\/li>\r\n<\/ol>\r\n
                                                                                                                  Exercise 5<\/h5>\r\n[latex]15x - 5=10x+45[\/latex]\r\n
                                                                                                                    \r\n \t
                                                                                                                  1. \u00a0[latex]2[\/latex]\r\n[reveal-answer q=\"318339\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"318339\"]no[\/hidden-answer]<\/li>\r\n \t
                                                                                                                  2. [latex]10[\/latex]\r\n[reveal-answer q=\"67141\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"67141\"]yes[\/hidden-answer]<\/li>\r\n<\/ol>\r\n
                                                                                                                    Exercise 6<\/h5>\r\n[latex]22p - 6=18p+86[\/latex]\r\n
                                                                                                                      \r\n \t
                                                                                                                    1. [latex]4[\/latex]<\/li>\r\n \t
                                                                                                                    2. [latex]23[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                      Model the Subtraction Property of Equality<\/h4>\r\nIn the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.\r\n\r\n\"This\r\n[reveal-answer q=\"890691\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"890691\"]x + 3 = 5; x = 2[\/hidden-answer]\r\n\r\n\"This\r\n

                                                                                                                      Solve Equations using the Subtraction Property of Equality<\/h4>\r\nIn the following exercises, solve each equation using the subtraction property of equality.\r\n
                                                                                                                        \r\n \t
                                                                                                                      1. [latex]c+8=14[\/latex]\r\n[reveal-answer q=\"402444\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"402444\"]6[\/hidden-answer]<\/li>\r\n \t
                                                                                                                      2. [latex]v+8=150[\/latex]<\/li>\r\n \t
                                                                                                                      3. [latex]23=x+12[\/latex]\r\n[reveal-answer q=\"266372\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"266372\"]11[\/hidden-answer]<\/li>\r\n \t
                                                                                                                      4. [latex]376=n+265[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                        Solve Equations using the Addition Property of Equality<\/h4>\r\nIn the following exercises, solve each equation using the addition property of equality.\r\n
                                                                                                                          \r\n \t
                                                                                                                        1. [latex]y - 7=16[\/latex]\r\n[reveal-answer q=\"937607\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"937607\"]23[\/hidden-answer]<\/li>\r\n \t
                                                                                                                        2. [latex]k - 42=113[\/latex]<\/li>\r\n \t
                                                                                                                        3. [latex]19=p - 15[\/latex]\r\n[reveal-answer q=\"166996\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"166996\"]34[\/hidden-answer]<\/li>\r\n \t
                                                                                                                        4. [latex]501=u - 399[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                          Translate English Sentences to Algebraic Equations<\/h4>\r\nIn the following exercises, translate each English sentence into an algebraic equation.\r\n
                                                                                                                            \r\n \t
                                                                                                                          1. The sum of [latex]7[\/latex] and [latex]33[\/latex] is equal to [latex]40[\/latex].\r\n[reveal-answer q=\"41132\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"41132\"]7 + 33 = 44[\/hidden-answer]<\/li>\r\n \t
                                                                                                                          2. The difference of [latex]15[\/latex] and [latex]3[\/latex] is equal to [latex]12[\/latex].<\/li>\r\n \t
                                                                                                                          3. The product of [latex]4[\/latex] and [latex]8[\/latex] is equal to [latex]32[\/latex].\r\n[reveal-answer q=\"248217\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"248217\"]4 \u22c5 8 = 32[\/hidden-answer]<\/li>\r\n \t
                                                                                                                          4. The quotient of [latex]63[\/latex] and [latex]9[\/latex] is equal to [latex]7[\/latex].<\/li>\r\n \t
                                                                                                                          5. Twice the difference of [latex]n[\/latex] and [latex]3[\/latex] gives [latex]76[\/latex].\r\n[reveal-answer q=\"103906\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"103906\"]2(n \u2212 3) = 76[\/hidden-answer]<\/li>\r\n \t
                                                                                                                          6. The sum of five times [latex]y[\/latex] and [latex]4[\/latex] is [latex]89[\/latex].<\/li>\r\n<\/ol>\r\n

                                                                                                                            Translate to an Equation and Solve<\/h4>\r\nIn the following exercises, translate each English sentence into an algebraic equation and then solve it.\r\n
                                                                                                                              \r\n \t
                                                                                                                            1. Eight more than [latex]x[\/latex] is equal to [latex]35[\/latex].\r\n[reveal-answer q=\"964989\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"964989\"]x + 8 = 35; x = 27[\/hidden-answer]<\/li>\r\n \t
                                                                                                                            2. [latex]21[\/latex] less than [latex]a[\/latex] is [latex]11[\/latex].<\/li>\r\n \t
                                                                                                                            3. The difference of [latex]q[\/latex] and [latex]18[\/latex] is [latex]57[\/latex].\r\n[reveal-answer q=\"296830\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"296830\"]q \u2212 18 = 57; q = 75[\/hidden-answer]<\/li>\r\n \t
                                                                                                                            4. The sum of [latex]m[\/latex] and [latex]125[\/latex] is [latex]240[\/latex].<\/li>\r\n<\/ol>\r\n

                                                                                                                              Mixed Practice<\/h4>\r\nIn the following exercises, solve each equation.\r\n
                                                                                                                                \r\n \t
                                                                                                                              1. [latex]h - 15=27[\/latex]\r\n[reveal-answer q=\"962508\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"962508\"]h = 42[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              2. [latex]k - 11=34[\/latex]<\/li>\r\n \t
                                                                                                                              3. [latex]z+52=85[\/latex]\r\n[reveal-answer q=\"391431\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"391431\"]z = 33[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              4. [latex]x+93=114[\/latex]<\/li>\r\n \t
                                                                                                                              5. [latex]27=q+19[\/latex]\r\n[reveal-answer q=\"216031\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"216031\"]q = 8[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              6. [latex]38=p+19[\/latex]<\/li>\r\n \t
                                                                                                                              7. [latex]31=v - 25[\/latex]\r\n[reveal-answer q=\"326035\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"326035\"]v = 56[\/hidden-answer]<\/li>\r\n \t
                                                                                                                              8. [latex]38=u - 16[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                \r\n

                                                                                                                                Finding Multiples and Factors<\/h3>\r\n

                                                                                                                                Identify Multiples of Numbers<\/h4>\r\nIn the following exercises, list all the multiples less than [latex]50[\/latex] for each of the following.\r\n
                                                                                                                                  \r\n \t
                                                                                                                                1. [latex]3[\/latex]\r\n[reveal-answer q=\"233737\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"233737\"]3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                2. [latex]2[\/latex]<\/li>\r\n \t
                                                                                                                                3. [latex]8[\/latex]\r\n[reveal-answer q=\"965317\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"965317\"]8, 16, 24, 32, 40, 48[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                4. [latex]10[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                  Use Common Divisibility Tests<\/h4>\r\nIn the following exercises, using the divisibility tests, determine whether each number is divisible by\u00a02, by\u00a03, by\u00a05, by\u00a06, and by\u00a010.\r\n
                                                                                                                                    \r\n \t
                                                                                                                                  1. [latex]96[\/latex]\r\n[reveal-answer q=\"921824\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"921824\"]2, 3, 6[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  2. [latex]250[\/latex]<\/li>\r\n \t
                                                                                                                                  3. [latex]420[\/latex]\r\n[reveal-answer q=\"843787\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"843787\"]2, 3, 5, 6, 10[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                  4. [latex]625[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                    Find All the Factors of a Number<\/h4>\r\nIn the following exercises, find all the factors of each number.\r\n
                                                                                                                                      \r\n \t
                                                                                                                                    1. [latex]30[\/latex]\r\n[reveal-answer q=\"820881\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"820881\"]1, 2, 3, 5, 6, 10, 15, 30[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    2. [latex]70[\/latex]<\/li>\r\n \t
                                                                                                                                    3. [latex]180[\/latex]\r\n[reveal-answer q=\"78969\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"78969\"]1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                    4. [latex]378[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                      Identify Prime and Composite Numbers<\/h4>\r\nIn the following exercises, identify each number as prime or composite.\r\n
                                                                                                                                        \r\n \t
                                                                                                                                      1. [latex]19[\/latex]\r\n[reveal-answer q=\"83860\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"83860\"]prime[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                      2. [latex]51[\/latex]<\/li>\r\n \t
                                                                                                                                      3. [latex]121[\/latex]\r\n[reveal-answer q=\"444866\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"444866\"]composite[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                      4. [latex]219[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                                                                                                                        \r\n

                                                                                                                                        Prime Factorization and the Least Common Multiple<\/h3>\r\n

                                                                                                                                        Find the Prime Factorization of a Composite Number<\/h4>\r\nIn the following exercises, find the prime factorization of each number.\r\n
                                                                                                                                          \r\n \t
                                                                                                                                        1. [latex]84[\/latex]\r\n[reveal-answer q=\"249507\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"249507\"]2 \u22c5 2 \u22c5 3 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                        2. [latex]165[\/latex]<\/li>\r\n \t
                                                                                                                                        3. [latex]350[\/latex]\r\n[reveal-answer q=\"718329\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"718329\"]2 \u22c5 5 \u22c5 5 \u22c5 7[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                        4. [latex]572[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                          Find the Least Common Multiple of Two Numbers<\/h4>\r\nIn the following exercises, find the least common multiple of each pair of numbers.\r\n
                                                                                                                                            \r\n \t
                                                                                                                                          1. [latex]9,15[\/latex]\r\n[reveal-answer q=\"293119\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"293119\"]45[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                          2. [latex]12,20[\/latex]<\/li>\r\n \t
                                                                                                                                          3. [latex]25,35[\/latex]\r\n[reveal-answer q=\"573498\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"573498\"]350[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                          4. [latex]18,40[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                                                            Everyday Math<\/h4>\r\nDescribe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n
                                                                                                                                            \r\n

                                                                                                                                            Chapter Practice Test<\/h3>\r\nIn the following exercises, translate from an algebraic equation to English phrases.\r\n
                                                                                                                                              \r\n \t
                                                                                                                                            1. [latex]6\\cdot 4[\/latex]<\/li>\r\n \t
                                                                                                                                            2. [latex]15-x[\/latex]\r\n[reveal-answer q=\"389557\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"389557\"]fifteen minus x[\/hidden-answer]<\/li>\r\n<\/ol>\r\nIn the following exercises, identify each as an expression or equation.\r\n
                                                                                                                                                \r\n \t
                                                                                                                                              1. [latex]5\\cdot 8+10[\/latex]<\/li>\r\n \t
                                                                                                                                              2. [latex]x+6=9[\/latex]\r\n[reveal-answer q=\"526716\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"526716\"]equation[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                              3. [latex]3\\cdot 11=33[\/latex]<\/li>\r\n \t
                                                                                                                                              4. Write [latex]n\\cdot n\\cdot n\\cdot n\\cdot n\\cdot n[\/latex] in exponential form.\r\n[reveal-answer q=\"78125\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"78125\"]n6<\/sup>[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                              5. Write [latex]{3}^{5}[\/latex] in expanded form and then simplify.\r\n[reveal-answer q=\"394981\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"394981\"]3 \u22c5 3 \u22c5 3 \u22c5 3 \u22c5 3 = 243[\/hidden-answer]<\/li>\r\n<\/ol>\r\nIn the following exercises, simplify, using the order of operations.\r\n
                                                                                                                                                  \r\n \t
                                                                                                                                                1. [latex]4+3\\cdot 5[\/latex]<\/li>\r\n \t
                                                                                                                                                2. [latex]\\left(8+1\\right)\\cdot 4[\/latex]\r\n[reveal-answer q=\"236893\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"236893\"]36[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                3. [latex]1+6\\left(3 - 1\\right)[\/latex]<\/li>\r\n \t
                                                                                                                                                4. [latex]\\left(8+4\\right)\\div 3+1[\/latex]\r\n[reveal-answer q=\"203290\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"203290\"]5[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                5. [latex]{\\left(1+4\\right)}^{2}[\/latex]<\/li>\r\n \t
                                                                                                                                                6. [latex]5\\left[2+7\\left(9 - 8\\right)\\right][\/latex]\r\n[reveal-answer q=\"581232\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"581232\"]45[\/hidden-answer]<\/li>\r\n<\/ol>\r\nIn the following exercises, evaluate each expression.\r\n
                                                                                                                                                    \r\n \t
                                                                                                                                                  1. [latex]8x - 3\\text{ when }x=4[\/latex]<\/li>\r\n \t
                                                                                                                                                  2. [latex]{y}^{3}\\text{ when }y=5[\/latex]\r\n[reveal-answer q=\"607430\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"607430\"]125[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                  3. [latex]6a - 2b\\text{ when }a=5,b=7[\/latex]<\/li>\r\n \t
                                                                                                                                                  4. [latex]hw\\text{ when }h=12,w=3[\/latex]\r\n[reveal-answer q=\"766583\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"766583\"]36[\/hidden-answer]<\/li>\r\n<\/ol>\r\nSimplify by combining like terms.\r\n
                                                                                                                                                      \r\n \t
                                                                                                                                                    1. \u00a0[latex]6x+8x[\/latex]<\/li>\r\n \t
                                                                                                                                                    2. [latex]9m+10+m+3[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, translate each phrase into an algebraic expression.\r\n
                                                                                                                                                        \r\n \t
                                                                                                                                                      1. [latex]5[\/latex] more than [latex]x[\/latex]\r\n[reveal-answer q=\"752665\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"752665\"]x + 5[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                      2. the quotient of [latex]12[\/latex] and [latex]y[\/latex]<\/li>\r\n \t
                                                                                                                                                      3. three times the difference of [latex]a\\text{ and }b[\/latex]\r\n[reveal-answer q=\"369566\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"369566\"]3(a \u2212 b)[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                      4. Caroline has [latex]3[\/latex] fewer earrings on her left ear than on her right ear. Call the number of earrings on her right ear, [latex]r[\/latex]. Write an expression for the number of earrings on her left ear.<\/li>\r\n<\/ol>\r\nIn the following exercises, solve each equation.\r\n
                                                                                                                                                          \r\n \t
                                                                                                                                                        1. [latex]n - 6=25[\/latex]\r\n[reveal-answer q=\"694048\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"694048\"]n = 31[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                        2. [latex]x+58=71[\/latex]<\/li>\r\n<\/ol>\r\nIn the following exercises, translate each English sentence into an algebraic equation and then solve it.\r\n
                                                                                                                                                            \r\n \t
                                                                                                                                                          1. [latex]15[\/latex] less than [latex]y[\/latex] is [latex]32[\/latex].\r\n[reveal-answer q=\"549973\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"549973\"]y \u2212 15 = 32; y = 47[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                          2. the sum of [latex]a[\/latex] and [latex]129[\/latex] is [latex]164[\/latex].<\/li>\r\n \t
                                                                                                                                                          3. List all the multiples of [latex]4[\/latex], that are less than [latex]50[\/latex].\r\n[reveal-answer q=\"353241\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"353241\"]4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                          4. Find all the factors of [latex]90[\/latex].<\/li>\r\n \t
                                                                                                                                                          5. Find the prime factorization of [latex]1080[\/latex].\r\n[reveal-answer q=\"30823\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"30823\"]23<\/sup> \u22c5 33<\/sup> \u22c5 5[\/hidden-answer]<\/li>\r\n \t
                                                                                                                                                          6. Find the LCM (Least Common Multiple) of [latex]24[\/latex] and [latex]40[\/latex].<\/li>\r\n<\/ol>\r\n<\/div>\r\n

                                                                                                                                                            Contribute!<\/h2>
                                                                                                                                                            Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"

                                                                                                                                                            Using the Language of Algebra<\/h2>\n

                                                                                                                                                            Use Variables and Algebraic Symbols<\/h3>\n

                                                                                                                                                            In the following exercises, translate from algebraic notation to words.<\/p>\n

                                                                                                                                                              \n
                                                                                                                                                            1. [latex]16 - 9[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              16 minus 9, the difference of sixteen and nine<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            2. [latex]25 - 7[\/latex]<\/li>\n
                                                                                                                                                            3. [latex]5\\cdot 6[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              5 times 6, the product of five and six<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            4. [latex]3\\cdot 9[\/latex]<\/li>\n
                                                                                                                                                            5. [latex]28\\div 4[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              28 divided by 4, the quotient of twenty-eight and four<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            6. [latex]45\\div 5[\/latex]<\/li>\n
                                                                                                                                                            7. [latex]x+8[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              x plus 8, the sum of x and eight<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            8. [latex]x+11[\/latex]<\/li>\n
                                                                                                                                                            9. [latex]\\left(2\\right)\\left(7\\right)[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              2 times 7, the product of two and seven<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            10. [latex]\\left(4\\right)\\left(8\\right)[\/latex]<\/li>\n
                                                                                                                                                            11. [latex]14<21[\/latex]\n\n\n
                                                                                                                                                              Show Solution<\/span>\n
                                                                                                                                                              fourteen is less than twenty-one<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            12. [latex]17<35[\/latex]<\/li>\n
                                                                                                                                                            13. [latex]36\\ge 19[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              thirty-six is greater than or equal to nineteen<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            14. [latex]42\\ge 27[\/latex]<\/li>\n
                                                                                                                                                            15. [latex]3n=24[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              3 times n equals 24, the product of three and n equals twenty-four<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            16. [latex]6n=36[\/latex]<\/li>\n
                                                                                                                                                            17. [latex]y - 1>6[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              y minus 1 is greater than 6, the difference of y and one is greater than six<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            18. [latex]y - 4>8[\/latex]<\/li>\n
                                                                                                                                                            19. [latex]2\\le 18\\div 6[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            20. [latex]3\\le 20\\div 4[\/latex]<\/li>\n
                                                                                                                                                            21. [latex]a\\ne 7\\cdot 4[\/latex]\n
                                                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                                                              a is not equal to 7 times 4, a is not equal to the product of seven and four<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                            22. [latex]a\\ne 1\\cdot 12[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                                              Identify<\/strong> Expressions and Equations<\/strong><\/h3>\n

                                                                                                                                                              In the following exercises, determine if each is an expression or an equation.<\/p>\n

                                                                                                                                                                \n
                                                                                                                                                              1. [latex]9\\cdot 6=54[\/latex]\n
                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                equation<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                              2. [latex]7\\cdot 9=63[\/latex]<\/li>\n
                                                                                                                                                              3. [latex]5\\cdot 4+3[\/latex]\n
                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                expression<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                              4. [latex]6\\cdot 3+5[\/latex]<\/li>\n
                                                                                                                                                              5. [latex]x+7[\/latex]\n
                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                expression<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                              6. [latex]x+9[\/latex]<\/li>\n
                                                                                                                                                              7. [latex]y - 5=25[\/latex]\n
                                                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                                                equation<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                              8. [latex]y - 8=32[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                                                Simplify Expressions with Exponents<\/h3>\n

                                                                                                                                                                In the following exercises, write in exponential form.<\/p>\n

                                                                                                                                                                  \n
                                                                                                                                                                1. [latex]3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3[\/latex]\n
                                                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                                                  37<\/sup><\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                2. [latex]4\\cdot 4\\cdot 4\\cdot 4\\cdot 4\\cdot 4[\/latex]<\/li>\n
                                                                                                                                                                3. [latex]x\\cdot x\\cdot x\\cdot x\\cdot x[\/latex]\n
                                                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                                                  x5<\/sup><\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                4. [latex]y\\cdot y\\cdot y\\cdot y\\cdot y\\cdot y[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                                                  Simplify Expressions with Exponents<\/h3>\n

                                                                                                                                                                  In the following exercises, write in expanded form.<\/p>\n

                                                                                                                                                                    \n
                                                                                                                                                                  1. [latex]{5}^{3}[\/latex]\n
                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                    125<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                  2. [latex]{8}^{3}[\/latex]<\/li>\n
                                                                                                                                                                  3. [latex]{2}^{8}[\/latex]\n
                                                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                                                    256<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                  4. [latex]{10}^{5}[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                                                    Simplify<\/strong> Expressions Using the Order of Operations<\/strong><\/h3>\n

                                                                                                                                                                    In the following exercises, simplify.<\/p>\n

                                                                                                                                                                      \n
                                                                                                                                                                    1. [latex]3+8\\cdot 5[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      43<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    2. [latex]\\text{(3+8)}\\cdot \\text{5}[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      55<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    3. [latex]2+6\\cdot 3[\/latex]<\/li>\n
                                                                                                                                                                    4. [latex]\\text{(2+6)}\\cdot \\text{3}[\/latex]<\/li>\n
                                                                                                                                                                    5. [latex]{2}^{3}-12\\div \\left(9 - 5\\right)[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      5<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    6. [latex]{3}^{2}-18\\div \\left(11 - 5\\right)[\/latex]<\/li>\n
                                                                                                                                                                    7. [latex]3\\cdot 8+5\\cdot 2[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      34<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    8. [latex]4\\cdot 7+3\\cdot 5[\/latex]<\/li>\n
                                                                                                                                                                    9. [latex]2+8\\left(6+1\\right)[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      58<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    10. [latex]4+6\\left(3+6\\right)[\/latex]<\/li>\n
                                                                                                                                                                    11. [latex]4\\cdot 12\/8[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      6<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    12. [latex]2\\cdot 36\/6[\/latex]<\/li>\n
                                                                                                                                                                    13. [latex]6+10\/2+2[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      13<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    14. [latex]9+12\/3+4[\/latex]<\/li>\n
                                                                                                                                                                    15. [latex]\\left(6+10\\right)\\div \\left(2+2\\right)[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      4<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    16. [latex]\\left(9+12\\right)\\div \\left(3+4\\right)[\/latex]<\/li>\n
                                                                                                                                                                    17. [latex]20\\div 4+6\\cdot 5[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      35<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    18. [latex]33\\div 3+8\\cdot 2[\/latex]<\/li>\n
                                                                                                                                                                    19. [latex]20\\div \\left(4+6\\right)\\cdot 5[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      10<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    20. [latex]33\\div \\left(3+8\\right)\\cdot 2[\/latex]<\/li>\n
                                                                                                                                                                    21. [latex]{4}^{2}+{5}^{2}[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      41<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    22. [latex]{3}^{2}+{7}^{2}[\/latex]<\/li>\n
                                                                                                                                                                    23. [latex]{\\left(4+5\\right)}^{2}[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      81<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    24. [latex]{\\left(3+7\\right)}^{2}[\/latex]<\/li>\n
                                                                                                                                                                    25. [latex]3\\left(1+9\\cdot 6\\right)-{4}^{2}[\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      149<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    26. [latex]5\\left(2+8\\cdot 4\\right)-{7}^{2}[\/latex]<\/li>\n
                                                                                                                                                                    27. [latex]2\\left[1+3\\left(10 - 2\\right)\\right][\/latex]\n
                                                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                                                      50<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                                                    28. [latex]5\\left[2+4\\left(3 - 2\\right)\\right][\/latex]<\/li>\n<\/ol>\n
                                                                                                                                                                      \n

                                                                                                                                                                      Everyday Math<\/h3>\n

                                                                                                                                                                      Basketball<\/h4>\n

                                                                                                                                                                      In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol [latex]\\text{(=},\\text{<},\\text{>)}[\/latex].<\/p>\n\n\n\n\n\n\n\n\n\n
                                                                                                                                                                      Spurs<\/strong><\/th>\nHeight<\/strong><\/th>\n<\/th>\nHeat<\/strong><\/th>\nHeight<\/strong><\/th>\n<\/tr>\n<\/thead>\n
                                                                                                                                                                      Tim Duncan<\/td>\n83″<\/td>\n<\/td>\nRashard Lewis<\/td>\n82″<\/td>\n<\/tr>\n
                                                                                                                                                                      Boris Diaw<\/td>\n80″<\/td>\nLeBron James<\/td>\n80″<\/td>\n<\/tr>\n
                                                                                                                                                                      Kawhi Leonard<\/td>\n79″<\/td>\nChris Bosh<\/td>\n83″<\/td>\n<\/tr>\n
                                                                                                                                                                      Tony Parker<\/td>\n74″<\/td>\nDwyane Wade<\/td>\n76″<\/td>\n<\/tr>\n
                                                                                                                                                                      Danny Green<\/td>\n78″<\/td>\nRay Allen<\/td>\n77″<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
                                                                                                                                                                        \n
                                                                                                                                                                      1. Height of Tim Duncan____Height of Rashard Lewis<\/li>\n
                                                                                                                                                                      2. Height of Boris Diaw____Height of LeBron James<\/li>\n
                                                                                                                                                                      3. Height of Kawhi Leonard____Height of Chris Bosh<\/li>\n
                                                                                                                                                                      4. Height of Tony Parker____Height of Dwyane Wade<\/li>\n
                                                                                                                                                                      5. Height of Danny Green____Height of Ray Allen<\/li>\n<\/ol>\n

                                                                                                                                                                        Elevation<\/h4>\n

                                                                                                                                                                        In Colorado there are more than [latex]50[\/latex] mountains with an elevation of over [latex]14,000\\text{ feet.}[\/latex] The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
                                                                                                                                                                        Mountain<\/th>\nElevation<\/th>\n<\/tr>\n<\/thead>\n
                                                                                                                                                                        Mt. Elbert<\/td>\n14,433′<\/td>\n<\/tr>\n
                                                                                                                                                                        Mt. Massive<\/td>\n14,421′<\/td>\n<\/tr>\n
                                                                                                                                                                        Mt. Harvard<\/td>\n14,420′<\/td>\n<\/tr>\n
                                                                                                                                                                        Blanca Peak<\/td>\n14,345′<\/td>\n<\/tr>\n
                                                                                                                                                                        La Plata Peak<\/td>\n14,336′<\/td>\n<\/tr>\n
                                                                                                                                                                        Uncompahgre Peak<\/td>\n14,309′<\/td>\n<\/tr>\n
                                                                                                                                                                        Crestone Peak<\/td>\n14,294′<\/td>\n<\/tr>\n
                                                                                                                                                                        Mt. Lincoln<\/td>\n14,286′<\/td>\n<\/tr>\n
                                                                                                                                                                        Grays Peak<\/td>\n14,270′<\/td>\n<\/tr>\n
                                                                                                                                                                        Mt. Antero<\/td>\n14,269′<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                                                                                                                                                        Elevation of La Plata Peak____Elevation of Mt. Antero
                                                                                                                                                                        \nElevation of Blanca Peak____Elevation of Mt. Elbert
                                                                                                                                                                        \nElevation of Gray\u2019s Peak____Elevation of Mt. Lincoln
                                                                                                                                                                        \nElevation of Mt. Massive____Elevation of Crestone Peak
                                                                                                                                                                        \nElevation of Mt. Harvard____Elevation of Uncompahgre Peak<\/p>\n<\/div>\n

                                                                                                                                                                        \n

                                                                                                                                                                        Writing Exercises<\/h3>\n

                                                                                                                                                                        Explain the difference between an expression and an equation.<\/p>\n