{"id":8990,"date":"2017-04-27T22:06:14","date_gmt":"2017-04-27T22:06:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8990"},"modified":"2020-07-02T05:42:53","modified_gmt":"2020-07-02T05:42:53","slug":"problem-set-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/problem-set-integers\/","title":{"raw":"Problem Set: Integers","rendered":"Problem Set: Integers"},"content":{"raw":"

Identifying and Writing Integers<\/h2>\r\n

Locate Positive and Negative Numbers on the Number Line<\/h3>\r\nIn the following exercises, locate and label the given points on a number line.\r\n

Exercise 1<\/h4>\r\n
    \r\n \t
  1. \u24d0 = [latex]2[\/latex]<\/li>\r\n \t
  2. \u24d1 = [latex]-2[\/latex]<\/li>\r\n \t
  3. \u24d2 = [latex]-5[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"263053\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"263053\"]\"This[\/hidden-answer]\r\n

    Exercise 2<\/h4>\r\n
      \r\n \t
    1. \u24d0 = [latex]5[\/latex]<\/li>\r\n \t
    2. \u24d1 = [latex]-5[\/latex]<\/li>\r\n \t
    3. \u24d2 = [latex]-2[\/latex]<\/li>\r\n<\/ol>\r\n

      Exercise 3<\/h4>\r\n
        \r\n \t
      1. \u24d0 = [latex]-8[\/latex]<\/li>\r\n \t
      2. \u24d1 = [latex]8[\/latex]<\/li>\r\n \t
      3. \u24d2 = [latex]-6[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"46772\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"46772\"]\"This[\/hidden-answer]\r\n

        Exercise 4<\/h4>\r\n
          \r\n \t
        1. \u24d0 = [latex]-7[\/latex]<\/li>\r\n \t
        2. \u24d1 = [latex]7[\/latex]<\/li>\r\n \t
        3. \u24d2 = [latex]-1[\/latex]<\/li>\r\n<\/ol>\r\n

          Order Positive and Negative Numbers on the Number Line<\/h3>\r\nIn the following exercises, order each of the following pairs of numbers, using < or >.\r\n
            \r\n \t
          1. [latex]9\\text{__}4[\/latex]\r\n[reveal-answer q=\"90623\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"90623\"] >[\/hidden-answer]<\/li>\r\n \t
          2. [latex]-3\\text{__}6[\/latex]\r\n[reveal-answer q=\"372663\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"372663\"]<[\/hidden-answer]<\/li>\r\n \t
          3. [latex]-8\\text{__}-2[\/latex]\r\n[reveal-answer q=\"988664\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"988664\"]<[\/hidden-answer]<\/li>\r\n \t
          4. [latex]1\\text{__}-10[\/latex]\r\n[reveal-answer q=\"420374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"420374\"]>[\/hidden-answer]<\/li>\r\n \t
          5. [latex]6\\text{__}2[\/latex]<\/li>\r\n \t
          6. [latex]-7\\text{__}4[\/latex]<\/li>\r\n \t
          7. [latex]-9\\text{__}-1[\/latex]<\/li>\r\n \t
          8. [latex]9\\text{__}-3[\/latex]<\/li>\r\n \t
          9. [latex]-5\\text{__}1[\/latex]\r\n[reveal-answer q=\"263929\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"263929\"]<[\/hidden-answer]<\/li>\r\n \t
          10. [latex]-4\\text{__}-9[\/latex]\r\n[reveal-answer q=\"708842\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"708842\"]>[\/hidden-answer]<\/li>\r\n \t
          11. [latex]6\\text{__}10[\/latex]\r\n[reveal-answer q=\"364908\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"364908\"]<[\/hidden-answer]<\/li>\r\n \t
          12. [latex]3\\text{__}-8[\/latex]\r\n[reveal-answer q=\"673039\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"673039\"]>[\/hidden-answer]<\/li>\r\n \t
          13. [latex]-7\\text{__}3[\/latex]<\/li>\r\n \t
          14. [latex]-10\\text{__}-5[\/latex]<\/li>\r\n \t
          15. [latex]2\\text{__}-6[\/latex]<\/li>\r\n \t
          16. [latex]8\\text{__}9[\/latex]<\/li>\r\n<\/ol>\r\n

            Find Opposites<\/h3>\r\nIn the following exercises, find the opposite of each number.\r\n
              \r\n \t
            1. [latex]2[\/latex]\r\n[reveal-answer q=\"986900\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"986900\"]\u22122[\/hidden-answer]<\/li>\r\n \t
            2. [latex]-6[\/latex]\r\n[reveal-answer q=\"968637\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"968637\"] 6[\/hidden-answer]<\/li>\r\n \t
            3. [latex]9[\/latex]<\/li>\r\n \t
            4. [latex]-4[\/latex]<\/li>\r\n \t
            5. [latex]-8[\/latex]\r\n[reveal-answer q=\"442811\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"442811\"] 8[\/hidden-answer]<\/li>\r\n \t
            6. [latex]1[\/latex]\r\n[reveal-answer q=\"613158\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"613158\"]-1[\/hidden-answer]<\/li>\r\n \t
            7. [latex]-2[\/latex]<\/li>\r\n \t
            8. [latex]6[\/latex]<\/li>\r\n<\/ol>\r\n

              Simplify Negatives<\/h3>\r\nIn the following exercises, simplify.\r\n
                \r\n \t
              1. [latex]-\\left(-4\\right)[\/latex]\r\n[reveal-answer q=\"788606\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"788606\"]4[\/hidden-answer]<\/li>\r\n \t
              2. [latex]-\\left(-8\\right)[\/latex]<\/li>\r\n \t
              3. [latex]-\\left(-15\\right)[\/latex]\r\n[reveal-answer q=\"236721\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"236721\"]15[\/hidden-answer]<\/li>\r\n \t
              4. [latex]-\\left(-11\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                Simplify Negatives<\/h3>\r\nIn the following exercises, evaluate.\r\n

                Exercise 1<\/h4>\r\n[latex]-m[\/latex] when\r\n
                  \r\n \t
                1. \u00a0[latex]m=3[\/latex]\r\n[reveal-answer q=\"469264\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"469264\"] \u22123[\/hidden-answer]<\/li>\r\n \t
                2. [latex]m=-3[\/latex]\r\n[reveal-answer q=\"249910\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"249910\"] 3[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                  Exercise 2<\/h4>\r\n[latex]-p[\/latex] when\r\n
                    \r\n \t
                  1. \u00a0[latex]p=6[\/latex]<\/li>\r\n \t
                  2. [latex]p=-6[\/latex]<\/li>\r\n<\/ol>\r\n

                    Exercise 3<\/h4>\r\n[latex]-c[\/latex] when\r\n
                      \r\n \t
                    1. \u00a0[latex]c=12[\/latex]\r\n[reveal-answer q=\"606524\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"606524\"]\u221212[\/hidden-answer]<\/li>\r\n \t
                    2. [latex]c=-12[\/latex]\r\n[reveal-answer q=\"753388\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"753388\"]12[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                      Exercise 3<\/h4>\r\n[latex]-d[\/latex] when\r\n
                        \r\n \t
                      1. [latex]d=21[\/latex]<\/li>\r\n \t
                      2. [latex]d=-21[\/latex]<\/li>\r\n<\/ol>\r\n

                        Simplify Expressions with Absolute Value<\/h3>\r\nIn the following exercises, simplify each absolute value expression.\r\n

                        Exercise 1<\/h4>\r\n
                          \r\n \t
                        1. [latex]|7|[\/latex]\r\n[reveal-answer q=\"18274\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"18274\"]7[\/hidden-answer]<\/li>\r\n \t
                        2. [latex]|-25|[\/latex]\r\n[reveal-answer q=\"135561\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"135561\"]25[\/hidden-answer]<\/li>\r\n \t
                        3. \u00a0[latex]|0|[\/latex]\r\n[reveal-answer q=\"464792\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"464792\"] 0[\/hidden-answer]<\/li>\r\n \t
                        4. \u00a0[latex]|5|[\/latex]<\/li>\r\n \t
                        5. \u00a0[latex]|20|[\/latex]<\/li>\r\n \t
                        6. \u00a0[latex]|-19|[\/latex]<\/li>\r\n \t
                        7. \u00a0[latex]|-32|[\/latex]\r\n[reveal-answer q=\"789833\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"789833\"]32[\/hidden-answer]<\/li>\r\n \t
                        8. [latex]|-18|[\/latex]\r\n[reveal-answer q=\"901130\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"901130\"]18[\/hidden-answer]<\/li>\r\n \t
                        9. \u00a0[latex]|16|[\/latex]\r\n[reveal-answer q=\"359206\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"359206\"]16[\/hidden-answer]<\/li>\r\n \t
                        10. [latex]|-41|[\/latex]<\/li>\r\n \t
                        11. \u00a0[latex]|-40|[\/latex]<\/li>\r\n \t
                        12. [latex]|22|[\/latex]<\/li>\r\n<\/ol>\r\n

                          Simplify Expressions with Absolute Value<\/h3>\r\nIn the following exercises, evaluate each absolute value expression.\r\n
                            \r\n \t
                          1. \u00a0[latex]|x|\\text{ when }x=-28[\/latex]\r\n[reveal-answer q=\"730673\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"730673\"]28[\/hidden-answer]<\/li>\r\n \t
                          2. \u00a0[latex]|-u|\\text{ when }u=-15[\/latex]\r\n[reveal-answer q=\"873122\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"873122\"]15[\/hidden-answer]<\/li>\r\n \t
                          3. [latex]|y|\\text{ when }y=-37[\/latex]<\/li>\r\n \t
                          4. [latex]|-z|\\text{ when }z=-24[\/latex]<\/li>\r\n \t
                          5. [latex]-|p|\\text{ when }p=19[\/latex]\r\n[reveal-answer q=\"713647\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"713647\"] \u221219[\/hidden-answer]<\/li>\r\n \t
                          6. [latex]-|q|\\text{ when }q=-33[\/latex]\r\n[reveal-answer q=\"866975\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"866975\"]\u221233[\/hidden-answer]<\/li>\r\n \t
                          7. [latex]-|a|\\text{ when }a=60[\/latex]<\/li>\r\n \t
                          8. [latex]-|b|\\text{ when }b=-12[\/latex]<\/li>\r\n<\/ol>\r\n

                            Simplify Expressions with Absolute Value<\/h3>\r\nIn the following exercises, fill in [latex]\\text{<},\\text{>},\\text{or}=[\/latex] to compare each expression.\r\n
                              \r\n \t
                            1. [latex]-6\\text{__}|-6|[\/latex]\r\n[reveal-answer q=\"431272\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"431272\"]<[\/hidden-answer]<\/li>\r\n \t
                            2. [latex]-|-3|\\text{__}-3[\/latex]\r\n[reveal-answer q=\"536598\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"536598\"]=[\/hidden-answer]<\/li>\r\n \t
                            3. [latex]-8\\text{__}|-8|[\/latex]<\/li>\r\n \t
                            4. [latex]-|-2|\\text{__}-2[\/latex]<\/li>\r\n \t
                            5. [latex]|-3|\\text{__}-|-3|[\/latex]\r\n[reveal-answer q=\"872309\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"872309\"]>[\/hidden-answer]<\/li>\r\n \t
                            6. [latex]4\\text{__}-|-4|[\/latex]\r\n[reveal-answer q=\"484575\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"484575\"]>[\/hidden-answer]<\/li>\r\n \t
                            7. [latex]|-5|\\text{__}-|-5|[\/latex]<\/li>\r\n \t
                            8. [latex]9\\text{__}-|-9|[\/latex]<\/li>\r\n<\/ol>\r\n

                              Simplify Expressions with Absolute Value<\/h3>\r\nIn the following exercises, simplify each expression.\r\n
                                \r\n \t
                              1. [latex]|8 - 4|[\/latex]\r\n[reveal-answer q=\"618767\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"618767\"]4[\/hidden-answer]<\/li>\r\n \t
                              2. [latex]|9 - 6|[\/latex]<\/li>\r\n \t
                              3. [latex]8|-7|[\/latex]\r\n[reveal-answer q=\"713390\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"713390\"]56[\/hidden-answer]<\/li>\r\n \t
                              4. [latex]5|-5|[\/latex]<\/li>\r\n \t
                              5. [latex]|15 - 7|-|14 - 6|[\/latex]\r\n[reveal-answer q=\"987783\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987783\"]0[\/hidden-answer]<\/li>\r\n \t
                              6. [latex]|17 - 8|-|13 - 4|[\/latex]<\/li>\r\n \t
                              7. [latex]18-|2\\left(8 - 3\\right)|[\/latex]\r\n[reveal-answer q=\"606475\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"606475\"]8[\/hidden-answer]<\/li>\r\n \t
                              8. [latex]15-|3\\left(8 - 5\\right)|[\/latex]<\/li>\r\n \t
                              9. [latex]8\\left(14 - 2|-2|\\right)[\/latex]\r\n[reveal-answer q=\"339040\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"339040\"]80[\/hidden-answer]<\/li>\r\n \t
                              10. [latex]6\\left(13 - 4|-2|\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                Translate Word Phrases into Expressions with Integers<\/h3>\r\nTranslate each phrase into an expression with integers. Do not simplify<\/em>.\r\n

                                Exercise 1<\/h4>\r\n
                                  \r\n \t
                                1. the opposite of [latex]8[\/latex]\r\n[reveal-answer q=\"376856\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"376856\"]\u22128[\/hidden-answer]<\/li>\r\n \t
                                2. the opposite of [latex]-6[\/latex]\r\n[reveal-answer q=\"728418\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"728418\"]\u2212(\u22126), or 6[\/hidden-answer]<\/li>\r\n \t
                                3. negative three\r\n[reveal-answer q=\"606913\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"606913\"]\u22123[\/hidden-answer]<\/li>\r\n \t
                                4. [latex]4[\/latex] minus negative [latex]3[\/latex]\r\n[reveal-answer q=\"595207\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"595207\"]4\u2212(\u22123)[\/hidden-answer]<\/li>\r\n \t
                                5. the opposite of [latex]11[\/latex]<\/li>\r\n \t
                                6. the opposite of [latex]-4[\/latex]<\/li>\r\n \t
                                7. negative nine<\/li>\r\n \t
                                8. [latex]8[\/latex] minus negative [latex]2[\/latex]<\/li>\r\n \t
                                9. the opposite of [latex]20[\/latex]\r\n[reveal-answer q=\"550221\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"550221\"]\u221220[\/hidden-answer]<\/li>\r\n \t
                                10. the opposite of [latex]-5[\/latex]\r\n[reveal-answer q=\"456015\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"456015\"]\u2212(\u22125), or 5[\/hidden-answer]<\/li>\r\n \t
                                11. the opposite of [latex]12[\/latex]\r\n[reveal-answer q=\"898230\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"898230\"]\u221212[\/hidden-answer]<\/li>\r\n \t
                                12. [latex]18[\/latex] minus negative [latex]7[\/latex]\r\n[reveal-answer q=\"791683\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"791683\"]18\u2212(\u22127)[\/hidden-answer]<\/li>\r\n \t
                                13. the opposite of [latex]15[\/latex]<\/li>\r\n \t
                                14. the opposite of [latex]-9[\/latex]<\/li>\r\n \t
                                15. negative sixty<\/li>\r\n \t
                                16. [latex]12[\/latex] minus [latex]5[\/latex]<\/li>\r\n \t
                                17. a temperature of [latex]6\\text{degrees}[\/latex] below zero\r\n[reveal-answer q=\"949671\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"949671\"]\u22126 degrees[\/hidden-answer]<\/li>\r\n \t
                                18. a temperature of [latex]14\\text{degrees}[\/latex] below zero<\/li>\r\n \t
                                19. an elevation of [latex]40\\text{ feet }[\/latex] below sea level\r\n[reveal-answer q=\"802949\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"802949\"]\u221240 feet[\/hidden-answer]<\/li>\r\n \t
                                20. an elevation of [latex]65\\text{ feet }[\/latex] below sea level<\/li>\r\n \t
                                21. a football play loss of [latex]12\\text{ yards }[\/latex]\r\n[reveal-answer q=\"485437\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"485437\"]\u221212 yards[\/hidden-answer]<\/li>\r\n \t
                                22. a football play gain of [latex]4\\text{ yards }[\/latex]<\/li>\r\n \t
                                23. a stock gain of [latex]\\$3[\/latex]\r\n[reveal-answer q=\"229637\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"229637\"]$3[\/hidden-answer]<\/li>\r\n \t
                                24. a stock loss of [latex]\\$5[\/latex]<\/li>\r\n \t
                                25. a golf score one above par\r\n[reveal-answer q=\"291954\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"291954\"]+1[\/hidden-answer]<\/li>\r\n \t
                                26. a golf score of [latex]3[\/latex] below par<\/li>\r\n<\/ol>\r\n
                                  \r\n

                                  Everyday Math<\/h3>\r\n

                                  Elevation<\/h4>\r\nThe highest elevation in the United States is Mount McKinley, Alaska, at [latex]20,320\\text{ feet}[\/latex] above sea level. The lowest elevation is Death Valley, California, at [latex]282\\text{ feet}[\/latex] below sea level. Use integers to write the elevation of:\r\n
                                    \r\n \t
                                  1. Mount McKinley\r\n[reveal-answer q=\"542287\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"542287\"]20,320 feet[\/hidden-answer]<\/li>\r\n \t
                                  2. Death Valley\r\n[reveal-answer q=\"826799\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"826799\"]\u2212282 feet[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                    Extreme temperatures<\/h4>\r\nThe highest recorded temperature on Earth is [latex]58^{\\circ}\\text{ Celsius}[\/latex], recorded in the Sahara Desert in 1922. The lowest recorded temperature is [latex]90^{\\circ}[\/latex] below [latex]0^{\\circ}\\text{ Celsius}[\/latex], recorded in Antarctica in 1983. Use integers to write the:\r\n
                                      \r\n \t
                                    1. \u00a0highest recorded temperature<\/li>\r\n \t
                                    2. lowest recorded temperature<\/li>\r\n<\/ol>\r\n

                                      State budgets<\/h4>\r\nIn June, 2011, the state of Pennsylvania estimated it would have a budget surplus of [latex]\\$540\\text{ million}[\/latex]. That same month, Texas estimated it would have a budget deficit of [latex]\\$27\\text{ billion}[\/latex]. Use integers to write the budget:\r\n
                                        \r\n \t
                                      1. surplus\r\n[reveal-answer q=\"339701\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"339701\"]$540 million[\/hidden-answer]<\/li>\r\n \t
                                      2. deficit\r\n[reveal-answer q=\"674481\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"674481\"]\u2212$27 billion[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                        College enrollments<\/h4>\r\nAcross the United States, community college enrollment grew by [latex]1,400,000[\/latex] students from [latex]2007[\/latex] to [latex]2010[\/latex]. In California, community college enrollment declined by [latex]110,171[\/latex] students from [latex]2009[\/latex] to [latex]2010[\/latex]. Use integers to write the change in enrollment:\r\n
                                          \r\n \t
                                        1. growth<\/li>\r\n \t
                                        2. decline<\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                          \r\n

                                          Writing Exercises<\/h3>\r\nGive an example of a negative number from your life experience.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"436283\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"436283\"]Sample answer: I have experienced negative temperatures.[\/hidden-answer]\r\n\r\nWhat are the three uses of the \"\u2212\" sign in algebra? Explain how they differ.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                          Adding Integers<\/h2>\r\n

                                          Model Addition of Integers<\/h3>\r\nIn the following exercises, model the expression to simplify.\r\n
                                            \r\n \t
                                          1. [latex]7+4[\/latex]\r\n[reveal-answer q=\"571959\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"571959\"]\"This\r\n11[\/hidden-answer]<\/li>\r\n \t
                                          2. [latex]8+5[\/latex]<\/li>\r\n \t
                                          3. [latex]-6+\\left(-3\\right)[\/latex]\r\n[reveal-answer q=\"995560\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"995560\"]\"This\r\n\u22129\u00a0[\/hidden-answer]<\/li>\r\n \t
                                          4. [latex]-5+\\left(-5\\right)[\/latex]<\/li>\r\n \t
                                          5. [latex]-7+5[\/latex]\r\n[reveal-answer q=\"875121\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"875121\"]\"This\r\n\u22122[\/hidden-answer]<\/li>\r\n \t
                                          6. [latex]-9+6[\/latex]<\/li>\r\n \t
                                          7. [latex]8+\\left(-7\\right)[\/latex]\r\n[reveal-answer q=\"384353\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"384353\"]\"This\r\n1 [\/hidden-answer]<\/li>\r\n \t
                                          8. [latex]9+\\left(-4\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                            Simplify Expressions with Integers<\/h3>\r\nIn the following exercises, simplify each expression.\r\n
                                              \r\n \t
                                            1. [latex]-21+\\left(-59\\right)[\/latex]\r\n[reveal-answer q=\"607103\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"607103\"]\u221280[\/hidden-answer]<\/li>\r\n \t
                                            2. [latex]-35+\\left(-47\\right)[\/latex]<\/li>\r\n \t
                                            3. [latex]48+\\left(-16\\right)[\/latex]\r\n[reveal-answer q=\"734026\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"734026\"]32[\/hidden-answer]<\/li>\r\n \t
                                            4. [latex]34+\\left(-19\\right)[\/latex]<\/li>\r\n \t
                                            5. [latex]-200+65[\/latex]\r\n[reveal-answer q=\"478369\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"478369\"]\u2212135[\/hidden-answer]<\/li>\r\n \t
                                            6. [latex]-150+45[\/latex]<\/li>\r\n \t
                                            7. [latex]2+\\left(-8\\right)+6[\/latex]\r\n[reveal-answer q=\"319290\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"319290\"]0[\/hidden-answer]<\/li>\r\n \t
                                            8. [latex]4+\\left(-9\\right)+7[\/latex]<\/li>\r\n \t
                                            9. [latex]-14+\\left(-12\\right)+4[\/latex]\r\n[reveal-answer q=\"747619\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"747619\"]\u221222[\/hidden-answer]<\/li>\r\n \t
                                            10. [latex]-17+\\left(-18\\right)+6[\/latex]<\/li>\r\n \t
                                            11. [latex]135+\\left(-110\\right)+83[\/latex]\r\n[reveal-answer q=\"393415\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"393415\"]108[\/hidden-answer]<\/li>\r\n \t
                                            12. [latex]140+\\left(-75\\right)+67[\/latex]<\/li>\r\n \t
                                            13. [latex]-32+24+\\left(-6\\right)+10[\/latex]\r\n[reveal-answer q=\"976823\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"976823\"]\u22124[\/hidden-answer]<\/li>\r\n \t
                                            14. [latex]-38+27+\\left(-8\\right)+12[\/latex]<\/li>\r\n \t
                                            15. [latex]19+2\\left(-3+8\\right)[\/latex]\r\n[reveal-answer q=\"916611\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"916611\"]29[\/hidden-answer]<\/li>\r\n \t
                                            16. [latex]24+3\\left(-5+9\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                              Evaluate Variable Expressions with Integers<\/h3>\r\nIn the following exercises, evaluate each expression.\r\n

                                              Exercise 1<\/h4>\r\n[latex]x+8[\/latex] when\r\n
                                                \r\n \t
                                              1. \u00a0[latex]x=-26[\/latex]\r\n[reveal-answer q=\"197824\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"197824\"] \u221218[\/hidden-answer]<\/li>\r\n \t
                                              2. [latex]x=-95[\/latex]\r\n[reveal-answer q=\"238483\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"238483\"]\u221287[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                Exercise 2<\/h4>\r\n[latex]y+9[\/latex] when\r\n
                                                  \r\n \t
                                                1. \u00a0[latex]y=-29[\/latex]<\/li>\r\n \t
                                                2. [latex]y=-84[\/latex]<\/li>\r\n<\/ol>\r\n

                                                  Exercise 3<\/h4>\r\n[latex]y+\\left(-14\\right)[\/latex] when\r\n
                                                    \r\n \t
                                                  1. [latex]y=-33[\/latex]\r\n[reveal-answer q=\"746629\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"746629\"]\u221247[\/hidden-answer]<\/li>\r\n \t
                                                  2. [latex]y=30[\/latex]\r\n[reveal-answer q=\"46278\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"46278\"]16[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                    Exercise 4<\/h4>\r\n[latex]x+\\left(-21\\right)[\/latex] when\r\n
                                                      \r\n \t
                                                    1. \u00a0[latex]x=-27[\/latex]<\/li>\r\n \t
                                                    2. [latex]x=44[\/latex]<\/li>\r\n<\/ol>\r\n

                                                      Exercise 5<\/h4>\r\nWhen [latex]a=-7[\/latex], evaluate:\r\n
                                                        \r\n \t
                                                      1. \u00a0[latex]a+3[\/latex]\r\n[reveal-answer q=\"672379\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"672379\"]\u22124[\/hidden-answer]<\/li>\r\n \t
                                                      2. [latex]-a+3[\/latex]\r\n[reveal-answer q=\"634316\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"634316\"]10[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                        Exercise 6<\/h4>\r\nWhen [latex]b=-11[\/latex], evaluate:\r\n
                                                          \r\n \t
                                                        1. [latex]b+6[\/latex]<\/li>\r\n \t
                                                        2. [latex]-b+6[\/latex]<\/li>\r\n<\/ol>\r\n

                                                          Exercise 7<\/h4>\r\nWhen [latex]c=-9[\/latex], evaluate:\r\n
                                                            \r\n \t
                                                          1. [latex]c+\\left(-4\\right)[\/latex]\r\n[reveal-answer q=\"225012\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225012\"]\u221213[\/hidden-answer]<\/li>\r\n \t
                                                          2. [latex]-c+\\left(-4\\right)[\/latex]\r\n[reveal-answer q=\"808238\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"808238\"]5[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                            Exercise 8<\/h4>\r\nWhen [latex]d=-8[\/latex], evaluate:\r\n
                                                              \r\n \t
                                                            1. [latex]d+\\left(-9\\right)[\/latex]<\/li>\r\n \t
                                                            2. [latex]-d+\\left(-9\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                              Evaluate Variable Expressions with Integers<\/h3>\r\nIn the following exercises, evaluate each expression.\r\n
                                                                \r\n \t
                                                              1. [latex]m+n[\/latex] when, [latex]m=-15[\/latex] , [latex]n=7[\/latex]\r\n[reveal-answer q=\"405224\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"405224\"]\u22128[\/hidden-answer]<\/li>\r\n \t
                                                              2. [latex]p+q[\/latex] when, [latex]p=-9[\/latex] , [latex]q=17[\/latex]<\/li>\r\n \t
                                                              3. [latex]r - 3s[\/latex] when, [latex]r=16[\/latex] , [latex]s=2[\/latex]\r\n[reveal-answer q=\"618922\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"618922\"]10[\/hidden-answer]<\/li>\r\n \t
                                                              4. [latex]2t+u[\/latex] when, [latex]t=-6[\/latex] , [latex]u=-5[\/latex]<\/li>\r\n \t
                                                              5. [latex]{\\left(a+b\\right)}^{2}[\/latex] when, [latex]a=-7[\/latex] , [latex]b=15[\/latex]\r\n[reveal-answer q=\"49812\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"49812\"]64[\/hidden-answer]<\/li>\r\n \t
                                                              6. [latex]{\\left(c+d\\right)}^{2}[\/latex] when, [latex]c=-5[\/latex] , [latex]d=14[\/latex]<\/li>\r\n \t
                                                              7. [latex]{\\left(x+y\\right)}^{2}[\/latex] when, [latex]x=-3[\/latex] , [latex]y=14[\/latex]\r\n[reveal-answer q=\"935743\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"935743\"]121[\/hidden-answer]<\/li>\r\n \t
                                                              8. [latex]{\\left(y+z\\right)}^{2}[\/latex] when, [latex]y=-3[\/latex] , [latex]z=15[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                Translate Word Phrases to Algebraic Expressions<\/h3>\r\nIn the following exercises, translate each phrase into an algebraic expression and then simplify.\r\n
                                                                  \r\n \t
                                                                1. The sum of [latex]-14[\/latex] and [latex]5[\/latex]\r\n[reveal-answer q=\"632402\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"632402\"]\u221214 + 5 = \u22129[\/hidden-answer]<\/li>\r\n \t
                                                                2. The sum of [latex]-22[\/latex] and [latex]9[\/latex]<\/li>\r\n \t
                                                                3. [latex]8[\/latex] more than [latex]-2[\/latex]\r\n[reveal-answer q=\"864650\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"864650\"]\u22122 + 8 = 6[\/hidden-answer]<\/li>\r\n \t
                                                                4. [latex]5[\/latex] more than [latex]-1[\/latex]<\/li>\r\n \t
                                                                5. [latex]-10[\/latex] added to [latex]-15[\/latex]\r\n[reveal-answer q=\"957890\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"957890\"]\u221215 + (\u221210) = \u221225[\/hidden-answer]<\/li>\r\n \t
                                                                6. [latex]-6[\/latex] added to [latex]-20[\/latex]<\/li>\r\n \t
                                                                7. [latex]6[\/latex] more than the sum of [latex]-1[\/latex] and [latex]-12[\/latex]\r\n[reveal-answer q=\"481142\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"481142\"][\u22121 + (\u221212)] + 6 = \u22127[\/hidden-answer]<\/li>\r\n \t
                                                                8. [latex]3[\/latex] more than the sum of [latex]-2[\/latex] and [latex]-8[\/latex]<\/li>\r\n \t
                                                                9. the sum of [latex]10[\/latex] and [latex]-19[\/latex], increased by [latex]4[\/latex]\r\n[reveal-answer q=\"201150\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"201150\"][10 + (\u221219)] + 4 = \u22125[\/hidden-answer]<\/li>\r\n \t
                                                                10. the sum of [latex]12[\/latex] and [latex]-15[\/latex], increased by [latex]1[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                  Add Integers in Applications<\/h3>\r\nIn the following exercises, solve.\r\n

                                                                  Temperature<\/h4>\r\nThe temperature in St. Paul, Minnesota was [latex]-19^{\\circ}\\text{ F}[\/latex] at sunrise. By noon the temperature had risen [latex]26^{\\circ}\\text{ F.}[\/latex] What was the temperature at noon?\r\n\r\n[reveal-answer q=\"627515\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"627515\"]7\u00b0F[\/hidden-answer]\r\n

                                                                  Temperature<\/h4>\r\nThe temperature in Chicago was [latex]-15^{\\circ}\\text{ F}[\/latex] at 6 am. By afternoon the temperature had risen [latex]28^{\\circ}\\text{ F}[\/latex]. What was the afternoon temperature?\r\n

                                                                  Credit Cards<\/h4>\r\nLupe owes [latex]\\$73[\/latex] on her credit card. Then she charges [latex]\\$45[\/latex] more. What is the new balance?\r\n\r\n[reveal-answer q=\"169912\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"169912\"]\u2212$118[\/hidden-answer]\r\n

                                                                  Credit Cards<\/h4>\r\nFrank owes [latex]\\$212[\/latex] on his credit card. Then he charges [latex]\\$105[\/latex] more. What is the new balance?\r\n

                                                                  Weight Loss<\/h4>\r\nAngie lost [latex]\\text{3 pounds}[\/latex] the first week of her diet. Over the next three weeks, she lost [latex]\\text{2 pounds,}[\/latex] gained [latex]\\text{1 pound,}[\/latex] and then lost [latex]\\text{4 pounds.}[\/latex] What was the change in her weight over the four weeks?\r\n

                                                                  Weight Loss<\/h4>\r\nApril lost [latex]\\text{5 pounds}[\/latex] the first week of her diet. Over the next three weeks, she lost [latex]\\text{3 pounds,}[\/latex] gained [latex]\\text{2 pounds,}[\/latex] and then lost [latex]\\text{1 pound.}[\/latex] What was the change in her weight over the four weeks?\r\n

                                                                  Football<\/h4>\r\nThe Rams took possession of the football on their own [latex]\\text{35-yard line.}[\/latex] In the next three plays, they lost [latex]\\text{12 yards,}[\/latex] gained [latex]\\text{8 yards,}[\/latex] then lost [latex]\\text{6 yards.}[\/latex] On what yard line was the ball at the end of those three plays?\r\n\r\n[reveal-answer q=\"150410\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"150410\"]25-yard line[\/hidden-answer]\r\n

                                                                  Football<\/h4>\r\nThe Cowboys began with the ball on their own [latex]\\text{20-yard line.}[\/latex] They gained [latex]\\text{15 yards,}[\/latex] lost [latex]\\text{3 yards}[\/latex] and then gained [latex]\\text{6 yards}[\/latex] on the next three plays. Where was the ball at the end of these plays?\r\n

                                                                  Calories<\/h4>\r\nLisbeth walked from her house to get a frozen yogurt, and then she walked home. By walking for a total of [latex]\\text{20 minutes,}[\/latex] she burned [latex]\\text{90 calories.}[\/latex] The frozen yogurt she ate was [latex]\\text{110 calories.}[\/latex] What was her total calorie gain or loss?\r\n\r\n[reveal-answer q=\"207433\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"207433\"]20 calories[\/hidden-answer]\r\n

                                                                  Calories<\/h4>\r\nOzzie rode his bike for [latex]\\text{30 minutes,}[\/latex] burning [latex]\\text{168 calories.}[\/latex] Then he had a [latex]\\text{140-calorie}[\/latex] iced blended mocha. Represent the change in calories as an integer.\r\n
                                                                  \r\n

                                                                  Everyday Math<\/h3>\r\n

                                                                  Stock Market<\/h4>\r\nThe week of September 15, 2008, was one of the most volatile weeks ever for the U.S. stock market. The change in the Dow Jones Industrial Average each day was:\r\n\r\n[latex]\\begin{array}{cccccc}\\text{Monday}\\hfill & -504\\hfill & \\text{Tuesday}\\hfill & +142\\hfill & \\text{Wednesday}\\hfill & -449\\hfill \\\\ \\text{Thursday}\\hfill & +410\\hfill & \\text{Friday}\\hfill & +369\\hfill & \\end{array}[\/latex]\r\n\r\nWhat was the overall change for the week?\r\n[reveal-answer q=\"130457\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"130457\"]\u221232[\/hidden-answer]\r\n

                                                                  Stock Market<\/h4>\r\nDuring the week of June 22, 2009, the change in the Dow Jones Industrial Average each day was:\r\n\r\n[latex]\\begin{array}{cccccc}\\text{Monday}\\hfill & -201\\hfill & \\text{Tuesday}\\hfill & -16\\hfill & \\text{Wednesday}\\hfill & -23\\hfill \\\\ \\text{Thursday}\\hfill & +172\\hfill & \\text{Friday}\\hfill & -34\\hfill & \\end{array}[\/latex]\r\n\r\nWhat was the overall change for the week?\r\n\r\n<\/div>\r\n
                                                                  \r\n

                                                                  Writing Exercises<\/h3>\r\nExplain why the sum of [latex]-8[\/latex] and [latex]\\text{2}[\/latex] is negative, but the sum of [latex]\\text{8}[\/latex] and [latex]-2[\/latex] and is positive.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"787668\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"787668\"]In the first case, there are more negatives so the sum is negative. In the second case, there are more positives so the sum is positive.[\/hidden-answer]\r\n\r\nGive an example from your life experience of adding two negative numbers.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                                  Subtracting Integers<\/h2>\r\n

                                                                  Model Subtraction of Integers<\/h3>\r\nIn the following exercises, model each expression and simplify.\r\n
                                                                    \r\n \t
                                                                  1. [latex]8 - 2[\/latex]\r\n[reveal-answer q=\"710244\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"710244\"]\"This\r\n6 [\/hidden-answer]<\/li>\r\n \t
                                                                  2. [latex]9 - 3[\/latex]<\/li>\r\n \t
                                                                  3. [latex]-5-\\left(-1\\right)[\/latex]\r\n[reveal-answer q=\"260036\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"260036\"]\"This\r\n\u20134 [\/hidden-answer]<\/li>\r\n \t
                                                                  4. [latex]-6-\\left(-4\\right)[\/latex]<\/li>\r\n \t
                                                                  5. [latex]-5 - 4[\/latex]\r\n[reveal-answer q=\"76875\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"76875\"]\"This\r\n\u20139 [\/hidden-answer]<\/li>\r\n \t
                                                                  6. [latex]-7 - 2[\/latex]<\/li>\r\n \t
                                                                  7. [latex]8-\\left(-4\\right)[\/latex]\r\n[reveal-answer q=\"76896\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"76896\"]\"This\r\n12\u00a0[\/hidden-answer]<\/li>\r\n \t
                                                                  8. [latex]7-\\left(-3\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                    Simplify Expressions with Integers<\/h3>\r\nIn the following exercises, simplify each expression.\r\n
                                                                      \r\n \t
                                                                    1. \u00a0[latex]15 - 6[\/latex]\r\n[reveal-answer q=\"843419\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"843419\"]9[\/hidden-answer]<\/li>\r\n \t
                                                                    2. [latex]15+\\left(-6\\right)[\/latex]\r\n[reveal-answer q=\"50604\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"50604\"]9[\/hidden-answer]<\/li>\r\n \t
                                                                    3. [latex]12 - 9[\/latex]<\/li>\r\n \t
                                                                    4. [latex]12+\\left(-9\\right)[\/latex]<\/li>\r\n \t
                                                                    5. [latex]44 - 28[\/latex]\r\n[reveal-answer q=\"415196\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"415196\"]16[\/hidden-answer]<\/li>\r\n \t
                                                                    6. [latex]44+\\left(-28\\right)[\/latex]\r\n[reveal-answer q=\"945526\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"945526\"]16[\/hidden-answer]<\/li>\r\n \t
                                                                    7. \u00a0[latex]35 - 16[\/latex]<\/li>\r\n \t
                                                                    8. [latex]35+\\left(-16\\right)[\/latex]<\/li>\r\n \t
                                                                    9. [latex]8-\\left(-9\\right)[\/latex]\r\n[reveal-answer q=\"990502\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"990502\"]17[\/hidden-answer]<\/li>\r\n \t
                                                                    10. [latex]8+9[\/latex]\r\n[reveal-answer q=\"878604\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"878604\"]17[\/hidden-answer]<\/li>\r\n \t
                                                                    11. [latex]4-\\left(-4\\right)[\/latex]<\/li>\r\n \t
                                                                    12. [latex]4+4[\/latex]<\/li>\r\n \t
                                                                    13. [latex]27-\\left(-18\\right)[\/latex]\r\n[reveal-answer q=\"131535\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"131535\"]45[\/hidden-answer]<\/li>\r\n \t
                                                                    14. [latex]27+18[\/latex]\r\n[reveal-answer q=\"202504\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"202504\"]45[\/hidden-answer]<\/li>\r\n \t
                                                                    15. [latex]46-\\left(-37\\right)[\/latex]<\/li>\r\n \t
                                                                    16. [latex]46+37[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                      Simplify Expressions with Integers<\/h3>\r\nIn the following exercises, simplify each expression.\r\n
                                                                        \r\n \t
                                                                      1. [latex]15-\\left(-12\\right)[\/latex]\r\n[reveal-answer q=\"244010\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"244010\"]27[\/hidden-answer]<\/li>\r\n \t
                                                                      2. [latex]14-\\left(-11\\right)[\/latex]<\/li>\r\n \t
                                                                      3. [latex]10-\\left(-19\\right)[\/latex]\r\n[reveal-answer q=\"597610\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"597610\"]29[\/hidden-answer]<\/li>\r\n \t
                                                                      4. [latex]11-\\left(-18\\right)[\/latex]<\/li>\r\n \t
                                                                      5. [latex]48 - 87[\/latex]\r\n[reveal-answer q=\"627293\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"627293\"]\u221239[\/hidden-answer]<\/li>\r\n \t
                                                                      6. [latex]45 - 69[\/latex]<\/li>\r\n \t
                                                                      7. [latex]31 - 79[\/latex]\r\n[reveal-answer q=\"483774\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"483774\"]\u221248[\/hidden-answer]<\/li>\r\n \t
                                                                      8. [latex]39 - 81[\/latex]<\/li>\r\n \t
                                                                      9. [latex]-31 - 11[\/latex]\r\n[reveal-answer q=\"687999\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"687999\"]\u221242[\/hidden-answer]<\/li>\r\n \t
                                                                      10. [latex]-32 - 18[\/latex]<\/li>\r\n \t
                                                                      11. [latex]-17 - 42[\/latex]\r\n[reveal-answer q=\"654482\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654482\"]\u221259[\/hidden-answer]<\/li>\r\n \t
                                                                      12. [latex]-19 - 46[\/latex]<\/li>\r\n \t
                                                                      13. [latex]-103-\\left(-52\\right)[\/latex]\r\n[reveal-answer q=\"654547\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654547\"]\u221251[\/hidden-answer]<\/li>\r\n \t
                                                                      14. [latex]-105-\\left(-68\\right)[\/latex]<\/li>\r\n \t
                                                                      15. [latex]-45-\\left(-54\\right)[\/latex]\r\n[reveal-answer q=\"357208\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"357208\"]9[\/hidden-answer]<\/li>\r\n \t
                                                                      16. [latex]-58-\\left(-67\\right)[\/latex]<\/li>\r\n \t
                                                                      17. [latex]8 - 3 - 7[\/latex]\r\n[reveal-answer q=\"363058\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"363058\"]\u22122[\/hidden-answer]<\/li>\r\n \t
                                                                      18. [latex]9 - 6 - 5[\/latex]<\/li>\r\n \t
                                                                      19. [latex]-5 - 4+7[\/latex]\r\n[reveal-answer q=\"875015\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"875015\"]\u22122[\/hidden-answer]<\/li>\r\n \t
                                                                      20. [latex]-3 - 8+4[\/latex]<\/li>\r\n \t
                                                                      21. [latex]-14-\\left(-27\\right)+9[\/latex]\r\n[reveal-answer q=\"197910\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"197910\"]22[\/hidden-answer]<\/li>\r\n \t
                                                                      22. [latex]-15-\\left(-28\\right)+5[\/latex]<\/li>\r\n \t
                                                                      23. [latex]71+\\left(-10\\right)-8[\/latex]\r\n[reveal-answer q=\"624234\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"624234\"]53[\/hidden-answer]<\/li>\r\n \t
                                                                      24. [latex]64+\\left(-17\\right)-9[\/latex]<\/li>\r\n \t
                                                                      25. [latex]-16-\\left(-4+1\\right)-7[\/latex]\r\n[reveal-answer q=\"213738\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"213738\"]\u221220[\/hidden-answer]<\/li>\r\n \t
                                                                      26. [latex]-15-\\left(-6+4\\right)-3[\/latex]<\/li>\r\n \t
                                                                      27. [latex]\\left(2 - 7\\right)-\\left(3 - 8\\right)[\/latex]\r\n[reveal-answer q=\"419994\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"419994\"]0[\/hidden-answer]<\/li>\r\n \t
                                                                      28. [latex]\\left(1 - 8\\right)-\\left(2 - 9\\right)[\/latex]<\/li>\r\n \t
                                                                      29. [latex]-\\left(6 - 8\\right)-\\left(2 - 4\\right)[\/latex]\r\n[reveal-answer q=\"931764\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"931764\"]4[\/hidden-answer]<\/li>\r\n \t
                                                                      30. [latex]-\\left(4 - 5\\right)-\\left(7 - 8\\right)[\/latex]<\/li>\r\n \t
                                                                      31. [latex]25-\\left[10-\\left(3 - 12\\right)\\right][\/latex]\r\n[reveal-answer q=\"443918\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"443918\"]6[\/hidden-answer]<\/li>\r\n \t
                                                                      32. [latex]32-\\left[5-\\left(15 - 20\\right)\\right][\/latex]<\/li>\r\n \t
                                                                      33. [latex]6\\cdot 3 - 4\\cdot 3 - 7\\cdot 2[\/latex]\r\n[reveal-answer q=\"631715\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"631715\"]\u22128[\/hidden-answer]<\/li>\r\n \t
                                                                      34. [latex]5\\cdot 7 - 8\\cdot 2 - 4\\cdot 9[\/latex]<\/li>\r\n \t
                                                                      35. [latex]{5}^{2}-{6}^{2}[\/latex]\r\n[reveal-answer q=\"427912\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"427912\"]\u221211[\/hidden-answer]<\/li>\r\n \t
                                                                      36. [latex]{6}^{2}-{7}^{2}[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                        Evaluate Variable Expressions with Integers<\/h3>\r\nIn the following exercises, evaluate each expression for the given values.\r\n

                                                                        Exercise 1<\/h4>\r\n[latex]x - 6\\text{ when }[\/latex]\r\n
                                                                          \r\n \t
                                                                        1. \u00a0[latex]x=3[\/latex]\r\n[reveal-answer q=\"519421\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"519421\"]-3[\/hidden-answer]<\/li>\r\n \t
                                                                        2. [latex]x=-3[\/latex]\r\n[reveal-answer q=\"304300\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"304300\"]\u22129[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                          Exercise 2<\/h4>\r\n[latex]x - 4\\text{ when }[\/latex]\r\n
                                                                            \r\n \t
                                                                          1. \u00a0[latex]x=5[\/latex]<\/li>\r\n \t
                                                                          2. [latex]x=-5[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                            Exercise 3<\/h4>\r\n[latex]5-y\\text{ when }[\/latex]\r\n
                                                                              \r\n \t
                                                                            1. [latex]y=2[\/latex]\r\n[reveal-answer q=\"761674\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"761674\"]3[\/hidden-answer]<\/li>\r\n \t
                                                                            2. [latex]y=-2[\/latex]\r\n[reveal-answer q=\"464780\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"464780\"]7[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                              Exercise 4<\/h4>\r\n[latex]8-y\\text{ when }[\/latex]\r\n
                                                                                \r\n \t
                                                                              1. \u00a0[latex]y=3[\/latex]<\/li>\r\n \t
                                                                              2. [latex]y=-3[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                Exercise 5<\/h4>\r\n
                                                                                  \r\n \t
                                                                                1. [latex]4{x}^{2}-15x+1\\text{ when }x=3[\/latex]\r\n[reveal-answer q=\"363334\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"363334\"]\u22128[\/hidden-answer]<\/li>\r\n \t
                                                                                2. [latex]5{x}^{2}-14x+7\\text{ when }x=2[\/latex]<\/li>\r\n \t
                                                                                3. [latex]-12 - 5{x}^{2}\\text{ when }x=6[\/latex]\r\n[reveal-answer q=\"553805\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"553805\"]\u2212192[\/hidden-answer]<\/li>\r\n \t
                                                                                4. [latex]-19 - 4{x}^{2}\\text{ when }x=5[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                  Translate Word Phrases to Algebraic Expressions<\/h3>\r\nIn the following exercises, translate each phrase into an algebraic expression and then simplify.\r\n
                                                                                    \r\n \t
                                                                                  1. The difference of [latex]3[\/latex] and [latex]-10[\/latex]\r\n[reveal-answer q=\"890458\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"890458\"]\u22123 \u2212 (\u221210) = 13[\/hidden-answer]<\/li>\r\n \t
                                                                                  2. Subtract [latex]-20[\/latex] from [latex]45[\/latex]\r\n[reveal-answer q=\"35474\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"35474\"]45 \u2212 (\u221220) = 65[\/hidden-answer]<\/li>\r\n \t
                                                                                  3. The difference of [latex]8[\/latex] and [latex]-12[\/latex]<\/li>\r\n \t
                                                                                  4. Subtract [latex]-13[\/latex] from [latex]50[\/latex]<\/li>\r\n \t
                                                                                  5. The difference of [latex]-6[\/latex] and [latex]9[\/latex]\r\n[reveal-answer q=\"693190\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"693190\"]\u22126 \u2212 9 = \u221215[\/hidden-answer]<\/li>\r\n \t
                                                                                  6. \u00a0Subtract [latex]-12[\/latex] from [latex]-16[\/latex]\r\n[reveal-answer q=\"374945\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"374945\"]\u221216 \u2212 (\u221212) = \u22124[\/hidden-answer]<\/li>\r\n \t
                                                                                  7. The difference of [latex]-8[\/latex] and [latex]9[\/latex]<\/li>\r\n \t
                                                                                  8. Subtract [latex]-15[\/latex] from [latex]-19[\/latex]<\/li>\r\n \t
                                                                                  9. [latex]8[\/latex] less than [latex]-17[\/latex]\r\n[reveal-answer q=\"59733\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"59733\"]\u221217 \u2212 8 = \u221225[\/hidden-answer]<\/li>\r\n \t
                                                                                  10. [latex]-24[\/latex] minus [latex]37[\/latex]\r\n[reveal-answer q=\"671321\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"671321\"]\u221224 \u2212 37 = \u221261[\/hidden-answer]<\/li>\r\n \t
                                                                                  11. [latex]5[\/latex] less than [latex]-14[\/latex]<\/li>\r\n \t
                                                                                  12. [latex]-13[\/latex] minus [latex]42[\/latex]<\/li>\r\n \t
                                                                                  13. [latex]21[\/latex] less than [latex]6[\/latex]\r\n[reveal-answer q=\"92563\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"92563\"] 6 \u2212 21 = \u221215[\/hidden-answer]<\/li>\r\n \t
                                                                                  14. [latex]31[\/latex] subtracted from [latex]-19[\/latex]\r\n[reveal-answer q=\"233689\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"233689\"]\u221219 \u2212 31 = \u221250[\/hidden-answer]<\/li>\r\n \t
                                                                                  15. [latex]34[\/latex] less than [latex]7[\/latex]<\/li>\r\n \t
                                                                                  16. [latex]29[\/latex] subtracted from [latex]-50[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                    Subtract Integers in Applications<\/h3>\r\nIn the following exercises, solve the following applications.\r\n

                                                                                    Temperature<\/h4>\r\nOne morning, the temperature in Urbana, Illinois, was [latex]28^{\\circ}\\text{ Fahrenheit}[\/latex]. By evening, the temperature had dropped [latex]38^{\\circ}\\text{ Fahrenheit}[\/latex]. What was the temperature that evening?\r\n\r\n[reveal-answer q=\"957328\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"957328\"]\u221210\u00b0[\/hidden-answer]\r\n

                                                                                    Temperature<\/h4>\r\nOn Thursday, the temperature in Spincich Lake, Michigan, was [latex]22^{\\circ}\\text{ Fahrenheit}[\/latex]. By Friday, the temperature had dropped [latex]35^{\\circ}\\text{ Fahrenheit}[\/latex]. What was the temperature on Friday?\r\n

                                                                                    Temperature<\/h4>\r\nOn January 15, the high temperature in Anaheim, California, was [latex]84^{\\circ}\\text{ Fahrenheit}[\/latex]. That same day, the high temperature in Embarrass, Minnesota was [latex]-12^{\\circ}\\text{ Fahrenheit}[\/latex]. What was the difference between the temperature in Anaheim and the temperature in Embarrass?\r\n\r\n[reveal-answer q=\"460126\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"460126\"]96\u00b0[\/hidden-answer]\r\n

                                                                                    Temperature<\/h4>\r\nOn January 21, the high temperature in Palm Springs, California, was [latex]89^{\\circ}[\/latex], and the high temperature in Whitefield, New Hampshire was [latex]-31^{\\circ}[\/latex]. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?\r\n

                                                                                    Football<\/h4>\r\nAt the first down, the Warriors football team had the ball on their [latex]30\\text{-yard line}[\/latex]. On the next three downs, they gained [latex]2\\text{ yards}[\/latex], lost [latex]7\\text{ yards}[\/latex], and lost [latex]4\\text{ yards}[\/latex]. What was the yard line at the end of the third down?\r\n\r\n[reveal-answer q=\"676409\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"676409\"]21-yard line[\/hidden-answer]\r\n

                                                                                    Football<\/h4>\r\nAt the first down, the Barons football team had the ball on their [latex]20\\text{-yard line}[\/latex]. On the next three downs, they lost [latex]\\text{8 yards,}[\/latex] gained [latex]5\\text{ yards}[\/latex], and lost [latex]6\\text{ yards}[\/latex]. What was the yard line at the end of the third down?\r\n

                                                                                    Checking Account<\/h4>\r\nJohn has [latex]\\$148[\/latex] in his checking account. He writes a check for [latex]\\$83[\/latex]. What is the new balance in his checking account?\r\n\r\n[reveal-answer q=\"274790\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"274790\"]$65[\/hidden-answer]\r\n

                                                                                    Checking Account<\/h4>\r\nEllie has [latex]\\$426[\/latex] in her checking account. She writes a check for [latex]\\$152[\/latex]. What is the new balance in her checking account?\r\n

                                                                                    Checking Account<\/h4>\r\nGina has [latex]\\$210[\/latex] in her checking account. She writes a check for [latex]\\$250[\/latex]. What is the new balance in her checking account?\r\n\r\n[reveal-answer q=\"987474\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987474\"]\u2212$40[\/hidden-answer]\r\n

                                                                                    Checking Account<\/h4>\r\nFrank has [latex]\\$94[\/latex] in his checking account. He writes a check for [latex]\\$110[\/latex]. What is the new balance in his checking account?\r\n

                                                                                    Checking Account<\/h4>\r\nBill has a balance of [latex]-\\$14[\/latex] in his checking account. He deposits [latex]\\$40[\/latex] to the account. What is the new balance?\r\n\r\n[reveal-answer q=\"188177\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"188177\"]$26[\/hidden-answer]\r\n

                                                                                    Checking Account<\/h4>\r\nPatty has a balance of [latex]-\\$23[\/latex] in her checking account. She deposits [latex]\\$80[\/latex] to the account. What is the new balance?\r\n
                                                                                    \r\n

                                                                                    Everyday Math<\/h3>\r\n

                                                                                    Camping<\/h4>\r\nRene is on an Alpine hike. The temperature is [latex]-7^{\\circ}[\/latex]. Rene\u2019s sleeping bag is rated \"comfortable to [latex]-20^{\\circ}[\/latex].\" How much can the temperature change before it is too cold for Rene\u2019s sleeping bag?\r\n\r\n[reveal-answer q=\"481762\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"481762\"]13\u00b0[\/hidden-answer]\r\n

                                                                                    Scuba Diving<\/h4>\r\nShelly\u2019s scuba watch is guaranteed to be watertight to [latex]-100\\text{ feet}[\/latex]. She is diving at [latex]-45\\text{ feet}[\/latex] on the face of an underwater canyon. By how many feet can she change her depth before her watch is no longer guaranteed?\r\n\r\n<\/div>\r\n
                                                                                    \r\n

                                                                                    Writing Exercises<\/h3>\r\nExplain why the difference of [latex]9[\/latex] and [latex]-6[\/latex] is [latex]15[\/latex].\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"888022\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"888022\"]Sample answer: On a number line, 9 is 15 units away from \u22126.[\/hidden-answer]\r\n\r\nWhy is the result of subtracting [latex]3-\\left(-4\\right)[\/latex] the same as the result of adding [latex]3+4?[\/latex]\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\n<\/div>\r\n

                                                                                    Multiplying and Dividing Integers<\/h2>\r\n

                                                                                    Multiply Integers<\/h3>\r\nIn the following exercises, multiply each pair of integers.\r\n
                                                                                      \r\n \t
                                                                                    1. [latex]-4\\cdot 8[\/latex]\r\n[reveal-answer q=\"269314\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"269314\"]\u221232[\/hidden-answer]<\/li>\r\n \t
                                                                                    2. [latex]-3\\cdot 9[\/latex]<\/li>\r\n \t
                                                                                    3. [latex]-5\\left(7\\right)[\/latex]\r\n[reveal-answer q=\"559696\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"559696\"]\u221235[\/hidden-answer]<\/li>\r\n \t
                                                                                    4. [latex]-8\\left(6\\right)[\/latex]<\/li>\r\n \t
                                                                                    5. [latex]-18\\left(-2\\right)[\/latex]\r\n[reveal-answer q=\"53301\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"53301\"]36[\/hidden-answer]<\/li>\r\n \t
                                                                                    6. [latex]-10\\left(-6\\right)[\/latex]<\/li>\r\n \t
                                                                                    7. [latex]9\\left(-7\\right)[\/latex]\r\n[reveal-answer q=\"298816\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"298816\"]\u221263[\/hidden-answer]<\/li>\r\n \t
                                                                                    8. [latex]13\\left(-5\\right)[\/latex]<\/li>\r\n \t
                                                                                    9. [latex]-1\\cdot 6[\/latex]\r\n[reveal-answer q=\"605920\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"605920\"]\u22126[\/hidden-answer]<\/li>\r\n \t
                                                                                    10. [latex]-1\\cdot 3[\/latex]<\/li>\r\n \t
                                                                                    11. [latex]-1\\left(-14\\right)[\/latex]\r\n[reveal-answer q=\"400280\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"400280\"]14[\/hidden-answer]<\/li>\r\n \t
                                                                                    12. [latex]-1\\left(-19\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                      Divide Integers<\/h3>\r\nIn the following exercises, divide.\r\n
                                                                                        \r\n \t
                                                                                      1. [latex]-24\\div 6[\/latex]\r\n[reveal-answer q=\"157385\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"157385\"]\u22124[\/hidden-answer]<\/li>\r\n \t
                                                                                      2. [latex]-28\\div 7[\/latex]<\/li>\r\n \t
                                                                                      3. [latex]56\\div \\left(-7\\right)[\/latex]\r\n[reveal-answer q=\"907169\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"907169\"]\u22128[\/hidden-answer]<\/li>\r\n \t
                                                                                      4. [latex]35\\div \\left(-7\\right)[\/latex]<\/li>\r\n \t
                                                                                      5. [latex]-52\\div \\left(-4\\right)[\/latex]\r\n[reveal-answer q=\"282992\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282992\"]13[\/hidden-answer]<\/li>\r\n \t
                                                                                      6. [latex]-84\\div \\left(-6\\right)[\/latex]<\/li>\r\n \t
                                                                                      7. [latex]-180\\div 15[\/latex]\r\n[reveal-answer q=\"41773\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"41773\"]\u221212[\/hidden-answer]<\/li>\r\n \t
                                                                                      8. [latex]-192\\div 12[\/latex]<\/li>\r\n \t
                                                                                      9. [latex]49\\div \\left(-1\\right)[\/latex]\r\n[reveal-answer q=\"623526\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"623526\"]\u221249[\/hidden-answer]<\/li>\r\n \t
                                                                                      10. [latex]62\\div \\left(-1\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                        Simplify Expressions with Integers<\/h3>\r\nIn the following exercises, simplify each expression.\r\n
                                                                                          \r\n \t
                                                                                        1. [latex]5\\left(-6\\right)+7\\left(-2\\right)-3[\/latex]\r\n[reveal-answer q=\"446481\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"446481\"]\u221247[\/hidden-answer]<\/li>\r\n \t
                                                                                        2. [latex]8\\left(-4\\right)+5\\left(-4\\right)-6[\/latex]<\/li>\r\n \t
                                                                                        3. [latex]-8\\left(-2\\right)-3\\left(-9\\right)[\/latex]\r\n[reveal-answer q=\"866322\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"866322\"]43[\/hidden-answer]<\/li>\r\n \t
                                                                                        4. [latex]-7\\left(-4\\right)-5\\left(-3\\right)[\/latex]<\/li>\r\n \t
                                                                                        5. [latex]{\\left(-5\\right)}^{3}[\/latex]\r\n[reveal-answer q=\"991071\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"991071\"]\u2212125[\/hidden-answer]<\/li>\r\n \t
                                                                                        6. [latex]{\\left(-4\\right)}^{3}[\/latex]<\/li>\r\n \t
                                                                                        7. [latex]{\\left(-2\\right)}^{6}[\/latex]\r\n[reveal-answer q=\"162966\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"162966\"]64[\/hidden-answer]<\/li>\r\n \t
                                                                                        8. [latex]{\\left(-3\\right)}^{5}[\/latex]<\/li>\r\n \t
                                                                                        9. [latex]-{4}^{2}[\/latex]\r\n[reveal-answer q=\"399641\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"399641\"]\u221216[\/hidden-answer]<\/li>\r\n \t
                                                                                        10. [latex]-{6}^{2}[\/latex]<\/li>\r\n \t
                                                                                        11. [latex]-3\\left(-5\\right)\\left(6\\right)[\/latex]\r\n[reveal-answer q=\"444587\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"444587\"]90[\/hidden-answer]<\/li>\r\n \t
                                                                                        12. [latex]-4\\left(-6\\right)\\left(3\\right)[\/latex]<\/li>\r\n \t
                                                                                        13. [latex]-4\\cdot 2\\cdot 11[\/latex]\r\n[reveal-answer q=\"422812\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"422812\"]\u221288[\/hidden-answer]<\/li>\r\n \t
                                                                                        14. [latex]-5\\cdot 3\\cdot 10[\/latex]<\/li>\r\n \t
                                                                                        15. [latex]\\left(8 - 11\\right)\\left(9 - 12\\right)[\/latex]\r\n[reveal-answer q=\"922291\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"922291\"]9[\/hidden-answer]<\/li>\r\n \t
                                                                                        16. [latex]\\left(6 - 11\\right)\\left(8 - 13\\right)[\/latex]<\/li>\r\n \t
                                                                                        17. [latex]26 - 3\\left(2 - 7\\right)[\/latex]\r\n[reveal-answer q=\"525176\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"525176\"]41[\/hidden-answer]<\/li>\r\n \t
                                                                                        18. [latex]23 - 2\\left(4 - 6\\right)[\/latex]<\/li>\r\n \t
                                                                                        19. [latex]-10\\left(-4\\right)\\div \\left(-8\\right)[\/latex]\r\n[reveal-answer q=\"499737\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"499737\"]\u22125[\/hidden-answer]<\/li>\r\n \t
                                                                                        20. [latex]-8\\left(-6\\right)\\div \\left(-4\\right)[\/latex]<\/li>\r\n \t
                                                                                        21. [latex]65\\div \\left(-5\\right)+\\left(-28\\right)\\div \\left(-7\\right)[\/latex]\r\n[reveal-answer q=\"348100\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"348100\"]\u22129[\/hidden-answer]<\/li>\r\n \t
                                                                                        22. [latex]52\\div \\left(-4\\right)+\\left(-32\\right)\\div \\left(-8\\right)[\/latex]<\/li>\r\n \t
                                                                                        23. [latex]9 - 2\\left[3 - 8\\left(-2\\right)\\right][\/latex]\r\n[reveal-answer q=\"125253\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"125253\"]\u221229[\/hidden-answer]<\/li>\r\n \t
                                                                                        24. [latex]11 - 3\\left[7 - 4\\left(-2\\right)\\right][\/latex]<\/li>\r\n \t
                                                                                        25. [latex]{\\left(-3\\right)}^{2}-24\\div \\left(8 - 2\\right)[\/latex]\r\n[reveal-answer q=\"393517\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"393517\"]5[\/hidden-answer]<\/li>\r\n \t
                                                                                        26. [latex]{\\left(-4\\right)}^{2}-32\\div \\left(12 - 4\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                          Evaluate Variable Expressions with Integers<\/h3>\r\nIn the following exercises, evaluate each expression.\r\n

                                                                                          Exercise 1<\/h4>\r\n[latex]-2x+17\\text{ when }[\/latex]\r\n
                                                                                            \r\n \t
                                                                                          1. \u00a0[latex]x=8[\/latex]\r\n[reveal-answer q=\"257663\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"257663\"]1[\/hidden-answer]<\/li>\r\n \t
                                                                                          2. [latex]x=-8[\/latex]\r\n[reveal-answer q=\"672473\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"672473\"]33[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                            Exercise 2<\/h4>\r\n[latex]-5y+14\\text{ when }[\/latex]\r\n
                                                                                              \r\n \t
                                                                                            1. [latex]y=9[\/latex]<\/li>\r\n \t
                                                                                            2. [latex]y=-9[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                              Exercise 3<\/h4>\r\n[latex]10 - 3m\\text{ when }[\/latex]\r\n
                                                                                                \r\n \t
                                                                                              1. [latex]m=5[\/latex]\r\n[reveal-answer q=\"636378\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"636378\"]\u22125[\/hidden-answer]<\/li>\r\n \t
                                                                                              2. [latex]m=-5[\/latex]\r\n[reveal-answer q=\"53523\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"53523\"]25[\/hidden-answer]<\/li>\r\n<\/ol>\r\n

                                                                                                Exercise 4<\/h4>\r\n
                                                                                                  \r\n \t
                                                                                                1. [latex]18 - 4n\\text{ when }[\/latex]<\/li>\r\n \t
                                                                                                2. [latex]n=3[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                  Exercise 5<\/h4>\r\n[latex]n=-3[\/latex]\r\n
                                                                                                    \r\n \t
                                                                                                  1. [latex]{p}^{2}-5p+5\\text{ when }p=-1[\/latex]\r\n[reveal-answer q=\"186134\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"186134\"]8[\/hidden-answer]<\/li>\r\n \t
                                                                                                  2. [latex]{q}^{2}-2q+9\\text{ when }q=-2[\/latex]<\/li>\r\n \t
                                                                                                  3. [latex]2{w}^{2}-3w+7\\text{ when }w=-2[\/latex]\r\n[reveal-answer q=\"75576\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"75576\"]21[\/hidden-answer]<\/li>\r\n \t
                                                                                                  4. [latex]3{u}^{2}-4u+5\\text{ when }u=-3[\/latex]<\/li>\r\n \t
                                                                                                  5. [latex]6x - 5y+15\\text{ when }x=3\\text{ and }y=-1[\/latex]\r\n[reveal-answer q=\"660399\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"660399\"]38[\/hidden-answer]<\/li>\r\n \t
                                                                                                  6. [latex]3p - 2q+9\\text{ when }p=8\\text{ and }q=-2[\/latex]<\/li>\r\n \t
                                                                                                  7. [latex]9a - 2b - 8\\text{ when }a=-6\\text{ and }b=-3[\/latex]\r\n[reveal-answer q=\"803693\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"803693\"]\u221256[\/hidden-answer]<\/li>\r\n \t
                                                                                                  8. [latex]7m - 4n - 2\\text{ when }m=-4\\text{ and }n=-9[\/latex]<\/li>\r\n<\/ol>\r\n

                                                                                                    Translate Word Phrases to Algebraic Expressions<\/h3>\r\nIn the following exercises, translate to an algebraic expression and simplify if possible.\r\n
                                                                                                      \r\n \t
                                                                                                    1. The product of [latex]-3[\/latex] and 15\r\n[reveal-answer q=\"285617\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"285617\"]\u22123\u00b715 = \u221245[\/hidden-answer]<\/li>\r\n \t
                                                                                                    2. The product of [latex]-4[\/latex] and [latex]16[\/latex]<\/li>\r\n \t
                                                                                                    3. The quotient of [latex]-60[\/latex] and [latex]-20[\/latex]\r\n[reveal-answer q=\"127917\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"127917\"]\u221260 \u00f7 (\u221220) = 3[\/hidden-answer]<\/li>\r\n \t
                                                                                                    4. The quotient of [latex]-40[\/latex] and [latex]-20[\/latex]<\/li>\r\n \t
                                                                                                    5. The quotient of [latex]-6[\/latex] and the sum of [latex]a[\/latex] and [latex]b[\/latex]\r\n[reveal-answer q=\"355795\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"355795\"][latex]\\Large\\frac{-6}{a+b}[\/latex][\/hidden-answer]<\/li>\r\n \t
                                                                                                    6. The quotient of [latex]-7[\/latex] and the sum of [latex]m[\/latex] and [latex]n[\/latex]<\/li>\r\n \t
                                                                                                    7. The product of [latex]-10[\/latex] and the difference of [latex]p\\text{ and }q[\/latex]\r\n[reveal-answer q=\"637649\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"637649\"]\u221210 (p \u2212 q)[\/hidden-answer]<\/li>\r\n \t
                                                                                                    8. The product of [latex]-13[\/latex] and the difference of [latex]c\\text{ and }d[\/latex]<\/li>\r\n<\/ol>\r\n
                                                                                                      \r\n

                                                                                                      Everyday Math<\/h3>\r\n

                                                                                                      Stock market<\/h4>\r\nJavier owns [latex]300[\/latex] shares of stock in one company. On Tuesday, the stock price dropped [latex]\\$12[\/latex] per share. What was the total effect on Javier\u2019s portfolio?\r\n\r\n[reveal-answer q=\"399802\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"399802\"]\u2013$3,600[\/hidden-answer]\r\n

                                                                                                      Weight loss<\/h4>\r\nIn the first week of a diet program, eight women lost an average of [latex]3\\text{ pounds}[\/latex] each. What was the total weight change for the eight women?\r\n\r\n<\/div>\r\n
                                                                                                      \r\n

                                                                                                      Writing Exercises<\/h3>\r\nIn your own words, state the rules for multiplying two integers.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"225671\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225671\"]Sample answer: Multiplying two integers with the same sign results in a positive product. Multiplying two integers with different signs results in a negative product.[\/hidden-answer]\r\n\r\nIn your own words, state the rules for dividing two integers.\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\r\nWhy is [latex]{-2}^{4}\\ne {\\left(-2\\right)}^{4}[\/latex]?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n[reveal-answer q=\"225672\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"225672\"]Sample answer: In one expression the base is positive and then we take the opposite, but in the other the base is negative.[\/hidden-answer]\r\n\r\nWhy is [latex]{-4}^{2}\\ne {\\left(-4\\right)}^{2}[\/latex]?\r\n\r\n[practice-area rows=\"4\"][\/practice-area]\r\n\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":"

                                                                                                      Identifying and Writing Integers<\/h2>\n

                                                                                                      Locate Positive and Negative Numbers on the Number Line<\/h3>\n

                                                                                                      In the following exercises, locate and label the given points on a number line.<\/p>\n

                                                                                                      Exercise 1<\/h4>\n
                                                                                                        \n
                                                                                                      1. \u24d0 = [latex]2[\/latex]<\/li>\n
                                                                                                      2. \u24d1 = [latex]-2[\/latex]<\/li>\n
                                                                                                      3. \u24d2 = [latex]-5[\/latex]<\/li>\n<\/ol>\n
                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                        \"This<\/div>\n<\/div>\n

                                                                                                        Exercise 2<\/h4>\n
                                                                                                          \n
                                                                                                        1. \u24d0 = [latex]5[\/latex]<\/li>\n
                                                                                                        2. \u24d1 = [latex]-5[\/latex]<\/li>\n
                                                                                                        3. \u24d2 = [latex]-2[\/latex]<\/li>\n<\/ol>\n

                                                                                                          Exercise 3<\/h4>\n
                                                                                                            \n
                                                                                                          1. \u24d0 = [latex]-8[\/latex]<\/li>\n
                                                                                                          2. \u24d1 = [latex]8[\/latex]<\/li>\n
                                                                                                          3. \u24d2 = [latex]-6[\/latex]<\/li>\n<\/ol>\n
                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                            \"This<\/div>\n<\/div>\n

                                                                                                            Exercise 4<\/h4>\n
                                                                                                              \n
                                                                                                            1. \u24d0 = [latex]-7[\/latex]<\/li>\n
                                                                                                            2. \u24d1 = [latex]7[\/latex]<\/li>\n
                                                                                                            3. \u24d2 = [latex]-1[\/latex]<\/li>\n<\/ol>\n

                                                                                                              Order Positive and Negative Numbers on the Number Line<\/h3>\n

                                                                                                              In the following exercises, order each of the following pairs of numbers, using < or >.<\/p>\n

                                                                                                                \n
                                                                                                              1. [latex]9\\text{__}4[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                ><\/div>\n<\/div>\n<\/li>\n
                                                                                                              2. [latex]-3\\text{__}6[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                <<\/div>\n<\/div>\n<\/li>\n
                                                                                                              3. [latex]-8\\text{__}-2[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                <<\/div>\n<\/div>\n<\/li>\n
                                                                                                              4. [latex]1\\text{__}-10[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                ><\/div>\n<\/div>\n<\/li>\n
                                                                                                              5. [latex]6\\text{__}2[\/latex]<\/li>\n
                                                                                                              6. [latex]-7\\text{__}4[\/latex]<\/li>\n
                                                                                                              7. [latex]-9\\text{__}-1[\/latex]<\/li>\n
                                                                                                              8. [latex]9\\text{__}-3[\/latex]<\/li>\n
                                                                                                              9. [latex]-5\\text{__}1[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                <<\/div>\n<\/div>\n<\/li>\n
                                                                                                              10. [latex]-4\\text{__}-9[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                ><\/div>\n<\/div>\n<\/li>\n
                                                                                                              11. [latex]6\\text{__}10[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                <<\/div>\n<\/div>\n<\/li>\n
                                                                                                              12. [latex]3\\text{__}-8[\/latex]\n
                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                ><\/div>\n<\/div>\n<\/li>\n
                                                                                                              13. [latex]-7\\text{__}3[\/latex]<\/li>\n
                                                                                                              14. [latex]-10\\text{__}-5[\/latex]<\/li>\n
                                                                                                              15. [latex]2\\text{__}-6[\/latex]<\/li>\n
                                                                                                              16. [latex]8\\text{__}9[\/latex]<\/li>\n<\/ol>\n

                                                                                                                Find Opposites<\/h3>\n

                                                                                                                In the following exercises, find the opposite of each number.<\/p>\n

                                                                                                                  \n
                                                                                                                1. [latex]2[\/latex]\n
                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                  \u22122<\/div>\n<\/div>\n<\/li>\n
                                                                                                                2. [latex]-6[\/latex]\n
                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                  6<\/div>\n<\/div>\n<\/li>\n
                                                                                                                3. [latex]9[\/latex]<\/li>\n
                                                                                                                4. [latex]-4[\/latex]<\/li>\n
                                                                                                                5. [latex]-8[\/latex]\n
                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                  8<\/div>\n<\/div>\n<\/li>\n
                                                                                                                6. [latex]1[\/latex]\n
                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                  -1<\/div>\n<\/div>\n<\/li>\n
                                                                                                                7. [latex]-2[\/latex]<\/li>\n
                                                                                                                8. [latex]6[\/latex]<\/li>\n<\/ol>\n

                                                                                                                  Simplify Negatives<\/h3>\n

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

                                                                                                                    \n
                                                                                                                  1. [latex]-\\left(-4\\right)[\/latex]\n
                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                    4<\/div>\n<\/div>\n<\/li>\n
                                                                                                                  2. [latex]-\\left(-8\\right)[\/latex]<\/li>\n
                                                                                                                  3. [latex]-\\left(-15\\right)[\/latex]\n
                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                    15<\/div>\n<\/div>\n<\/li>\n
                                                                                                                  4. [latex]-\\left(-11\\right)[\/latex]<\/li>\n<\/ol>\n

                                                                                                                    Simplify Negatives<\/h3>\n

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

                                                                                                                    Exercise 1<\/h4>\n

                                                                                                                    [latex]-m[\/latex] when<\/p>\n

                                                                                                                      \n
                                                                                                                    1. \u00a0[latex]m=3[\/latex]\n
                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                      \u22123<\/div>\n<\/div>\n<\/li>\n
                                                                                                                    2. [latex]m=-3[\/latex]\n
                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                      3<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                      Exercise 2<\/h4>\n

                                                                                                                      [latex]-p[\/latex] when<\/p>\n

                                                                                                                        \n
                                                                                                                      1. \u00a0[latex]p=6[\/latex]<\/li>\n
                                                                                                                      2. [latex]p=-6[\/latex]<\/li>\n<\/ol>\n

                                                                                                                        Exercise 3<\/h4>\n

                                                                                                                        [latex]-c[\/latex] when<\/p>\n

                                                                                                                          \n
                                                                                                                        1. \u00a0[latex]c=12[\/latex]\n
                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                          \u221212<\/div>\n<\/div>\n<\/li>\n
                                                                                                                        2. [latex]c=-12[\/latex]\n
                                                                                                                          Show Solution<\/span><\/p>\n
                                                                                                                          12<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                          Exercise 3<\/h4>\n

                                                                                                                          [latex]-d[\/latex] when<\/p>\n

                                                                                                                            \n
                                                                                                                          1. [latex]d=21[\/latex]<\/li>\n
                                                                                                                          2. [latex]d=-21[\/latex]<\/li>\n<\/ol>\n

                                                                                                                            Simplify Expressions with Absolute Value<\/h3>\n

                                                                                                                            In the following exercises, simplify each absolute value expression.<\/p>\n

                                                                                                                            Exercise 1<\/h4>\n
                                                                                                                              \n
                                                                                                                            1. [latex]|7|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              7<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            2. [latex]|-25|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              25<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            3. \u00a0[latex]|0|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              0<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            4. \u00a0[latex]|5|[\/latex]<\/li>\n
                                                                                                                            5. \u00a0[latex]|20|[\/latex]<\/li>\n
                                                                                                                            6. \u00a0[latex]|-19|[\/latex]<\/li>\n
                                                                                                                            7. \u00a0[latex]|-32|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              32<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            8. [latex]|-18|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              18<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            9. \u00a0[latex]|16|[\/latex]\n
                                                                                                                              Show Solution<\/span><\/p>\n
                                                                                                                              16<\/div>\n<\/div>\n<\/li>\n
                                                                                                                            10. [latex]|-41|[\/latex]<\/li>\n
                                                                                                                            11. \u00a0[latex]|-40|[\/latex]<\/li>\n
                                                                                                                            12. [latex]|22|[\/latex]<\/li>\n<\/ol>\n

                                                                                                                              Simplify Expressions with Absolute Value<\/h3>\n

                                                                                                                              In the following exercises, evaluate each absolute value expression.<\/p>\n

                                                                                                                                \n
                                                                                                                              1. \u00a0[latex]|x|\\text{ when }x=-28[\/latex]\n
                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                28<\/div>\n<\/div>\n<\/li>\n
                                                                                                                              2. \u00a0[latex]|-u|\\text{ when }u=-15[\/latex]\n
                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                15<\/div>\n<\/div>\n<\/li>\n
                                                                                                                              3. [latex]|y|\\text{ when }y=-37[\/latex]<\/li>\n
                                                                                                                              4. [latex]|-z|\\text{ when }z=-24[\/latex]<\/li>\n
                                                                                                                              5. [latex]-|p|\\text{ when }p=19[\/latex]\n
                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                \u221219<\/div>\n<\/div>\n<\/li>\n
                                                                                                                              6. [latex]-|q|\\text{ when }q=-33[\/latex]\n
                                                                                                                                Show Solution<\/span><\/p>\n
                                                                                                                                \u221233<\/div>\n<\/div>\n<\/li>\n
                                                                                                                              7. [latex]-|a|\\text{ when }a=60[\/latex]<\/li>\n
                                                                                                                              8. [latex]-|b|\\text{ when }b=-12[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                Simplify Expressions with Absolute Value<\/h3>\n

                                                                                                                                In the following exercises, fill in [latex]\\text{<},\\text{>},\\text{or}=[\/latex] to compare each expression.<\/p>\n

                                                                                                                                  \n
                                                                                                                                1. [latex]-6\\text{__}|-6|[\/latex]\n
                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                  <<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                2. [latex]-|-3|\\text{__}-3[\/latex]\n
                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                  =<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                3. [latex]-8\\text{__}|-8|[\/latex]<\/li>\n
                                                                                                                                4. [latex]-|-2|\\text{__}-2[\/latex]<\/li>\n
                                                                                                                                5. [latex]|-3|\\text{__}-|-3|[\/latex]\n
                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                  ><\/div>\n<\/div>\n<\/li>\n
                                                                                                                                6. [latex]4\\text{__}-|-4|[\/latex]\n
                                                                                                                                  Show Solution<\/span><\/p>\n
                                                                                                                                  ><\/div>\n<\/div>\n<\/li>\n
                                                                                                                                7. [latex]|-5|\\text{__}-|-5|[\/latex]<\/li>\n
                                                                                                                                8. [latex]9\\text{__}-|-9|[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                  Simplify Expressions with Absolute Value<\/h3>\n

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

                                                                                                                                    \n
                                                                                                                                  1. [latex]|8 - 4|[\/latex]\n
                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                    4<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                  2. [latex]|9 - 6|[\/latex]<\/li>\n
                                                                                                                                  3. [latex]8|-7|[\/latex]\n
                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                    56<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                  4. [latex]5|-5|[\/latex]<\/li>\n
                                                                                                                                  5. [latex]|15 - 7|-|14 - 6|[\/latex]\n
                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                    0<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                  6. [latex]|17 - 8|-|13 - 4|[\/latex]<\/li>\n
                                                                                                                                  7. [latex]18-|2\\left(8 - 3\\right)|[\/latex]\n
                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                    8<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                  8. [latex]15-|3\\left(8 - 5\\right)|[\/latex]<\/li>\n
                                                                                                                                  9. [latex]8\\left(14 - 2|-2|\\right)[\/latex]\n
                                                                                                                                    Show Solution<\/span><\/p>\n
                                                                                                                                    80<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                  10. [latex]6\\left(13 - 4|-2|\\right)[\/latex]<\/li>\n<\/ol>\n

                                                                                                                                    Translate Word Phrases into Expressions with Integers<\/h3>\n

                                                                                                                                    Translate each phrase into an expression with integers. Do not simplify<\/em>.<\/p>\n

                                                                                                                                    Exercise 1<\/h4>\n
                                                                                                                                      \n
                                                                                                                                    1. the opposite of [latex]8[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u22128<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    2. the opposite of [latex]-6[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u2212(\u22126), or 6<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    3. negative three\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u22123<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    4. [latex]4[\/latex] minus negative [latex]3[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      4\u2212(\u22123)<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    5. the opposite of [latex]11[\/latex]<\/li>\n
                                                                                                                                    6. the opposite of [latex]-4[\/latex]<\/li>\n
                                                                                                                                    7. negative nine<\/li>\n
                                                                                                                                    8. [latex]8[\/latex] minus negative [latex]2[\/latex]<\/li>\n
                                                                                                                                    9. the opposite of [latex]20[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u221220<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    10. the opposite of [latex]-5[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u2212(\u22125), or 5<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    11. the opposite of [latex]12[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u221212<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    12. [latex]18[\/latex] minus negative [latex]7[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      18\u2212(\u22127)<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    13. the opposite of [latex]15[\/latex]<\/li>\n
                                                                                                                                    14. the opposite of [latex]-9[\/latex]<\/li>\n
                                                                                                                                    15. negative sixty<\/li>\n
                                                                                                                                    16. [latex]12[\/latex] minus [latex]5[\/latex]<\/li>\n
                                                                                                                                    17. a temperature of [latex]6\\text{degrees}[\/latex] below zero\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u22126 degrees<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    18. a temperature of [latex]14\\text{degrees}[\/latex] below zero<\/li>\n
                                                                                                                                    19. an elevation of [latex]40\\text{ feet }[\/latex] below sea level\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u221240 feet<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    20. an elevation of [latex]65\\text{ feet }[\/latex] below sea level<\/li>\n
                                                                                                                                    21. a football play loss of [latex]12\\text{ yards }[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      \u221212 yards<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    22. a football play gain of [latex]4\\text{ yards }[\/latex]<\/li>\n
                                                                                                                                    23. a stock gain of [latex]\\$3[\/latex]\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      $3<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    24. a stock loss of [latex]\\$5[\/latex]<\/li>\n
                                                                                                                                    25. a golf score one above par\n
                                                                                                                                      Show Solution<\/span><\/p>\n
                                                                                                                                      +1<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                    26. a golf score of [latex]3[\/latex] below par<\/li>\n<\/ol>\n
                                                                                                                                      \n

                                                                                                                                      Everyday Math<\/h3>\n

                                                                                                                                      Elevation<\/h4>\n

                                                                                                                                      The highest elevation in the United States is Mount McKinley, Alaska, at [latex]20,320\\text{ feet}[\/latex] above sea level. The lowest elevation is Death Valley, California, at [latex]282\\text{ feet}[\/latex] below sea level. Use integers to write the elevation of:<\/p>\n

                                                                                                                                        \n
                                                                                                                                      1. Mount McKinley\n
                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                        20,320 feet<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                      2. Death Valley\n
                                                                                                                                        Show Solution<\/span><\/p>\n
                                                                                                                                        \u2212282 feet<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                        Extreme temperatures<\/h4>\n

                                                                                                                                        The highest recorded temperature on Earth is [latex]58^{\\circ}\\text{ Celsius}[\/latex], recorded in the Sahara Desert in 1922. The lowest recorded temperature is [latex]90^{\\circ}[\/latex] below [latex]0^{\\circ}\\text{ Celsius}[\/latex], recorded in Antarctica in 1983. Use integers to write the:<\/p>\n

                                                                                                                                          \n
                                                                                                                                        1. \u00a0highest recorded temperature<\/li>\n
                                                                                                                                        2. lowest recorded temperature<\/li>\n<\/ol>\n

                                                                                                                                          State budgets<\/h4>\n

                                                                                                                                          In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of [latex]\\$540\\text{ million}[\/latex]. That same month, Texas estimated it would have a budget deficit of [latex]\\$27\\text{ billion}[\/latex]. Use integers to write the budget:<\/p>\n

                                                                                                                                            \n
                                                                                                                                          1. surplus\n
                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                            $540 million<\/div>\n<\/div>\n<\/li>\n
                                                                                                                                          2. deficit\n
                                                                                                                                            Show Solution<\/span><\/p>\n
                                                                                                                                            \u2212$27 billion<\/div>\n<\/div>\n<\/li>\n<\/ol>\n

                                                                                                                                            College enrollments<\/h4>\n

                                                                                                                                            Across the United States, community college enrollment grew by [latex]1,400,000[\/latex] students from [latex]2007[\/latex] to [latex]2010[\/latex]. In California, community college enrollment declined by [latex]110,171[\/latex] students from [latex]2009[\/latex] to [latex]2010[\/latex]. Use integers to write the change in enrollment:<\/p>\n

                                                                                                                                              \n
                                                                                                                                            1. growth<\/li>\n
                                                                                                                                            2. decline<\/li>\n<\/ol>\n<\/div>\n
                                                                                                                                              \n

                                                                                                                                              Writing Exercises<\/h3>\n

                                                                                                                                              Give an example of a negative number from your life experience.<\/p>\n