{"id":8959,"date":"2017-04-27T21:44:44","date_gmt":"2017-04-27T21:44:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8959"},"modified":"2019-08-16T21:29:47","modified_gmt":"2019-08-16T21:29:47","slug":"problem-set-solving-linear-equations-part-i","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/problem-set-solving-linear-equations-part-i\/","title":{"raw":"Problem Set: Multi-Step Linear Equations","rendered":"Problem Set: Multi-Step Linear Equations"},"content":{"raw":"

THIS IS OPTIONAL ADDITIONAL PRACTICE<\/h3>\r\n

Solve Equations Using the Subtraction and Addition Properties of Equality<\/h2>\r\nIn the following exercises, determine whether the given value is a solution to the equation.\r\n\r\nIs [latex]y=\\Large\\frac{1}{3}[\/latex] a solution of [latex]4y+2=10y?[\/latex]\r\n\r\nyes\r\n\r\nIs [latex]x=\\Large\\frac{3}{4}[\/latex] a solution of [latex]5x+3=9x?[\/latex]\r\n\r\nIs [latex]u=-\\Large\\frac{1}{2}[\/latex] a solution of [latex]8u - 1=6u?[\/latex]\r\n\r\nno\r\n\r\nIs [latex]v=-\\Large\\frac{1}{3}[\/latex] a solution of [latex]9v - 2=3v?[\/latex]\r\n\r\nIn the following exercises, solve each equation.\r\n\r\n[latex]x+7=12[\/latex]\r\n\r\nx<\/em> = 5\r\n\r\n[latex]y+5=-6[\/latex]\r\n\r\n[latex]b+\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]b=\\Large\\frac{1}{2}[\/latex]\r\n\r\n[latex]a+\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{4}{5}[\/latex]\r\n\r\n[latex]p+2.4=-9.3[\/latex]\r\n\r\np<\/em> = \u221211.7\r\n\r\n[latex]m+7.9=11.6[\/latex]\r\n\r\n[latex]a - 3=7[\/latex]\r\n\r\na<\/em> = 10\r\n\r\n[latex]m - 8=-20[\/latex]\r\n\r\n[latex]x-\\Large\\frac{1}{3}\\normalsize=2[\/latex]\r\n\r\n[latex]x=\\Large\\frac{7}{3}[\/latex]\r\n\r\n[latex]x-\\Large\\frac{1}{5}\\normalsize =4[\/latex]\r\n\r\n[latex]y - 3.8=10[\/latex]\r\n\r\ny<\/em> = 13.8\r\n\r\n[latex]y - 7.2=5[\/latex]\r\n\r\n[latex]x - 15=-42[\/latex]\r\n\r\nx<\/em> = \u221227\r\n\r\n[latex]z+5.2=-8.5[\/latex]\r\n\r\n[latex]q+\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{1}{2}[\/latex]\r\n\r\n[latex]q=-\\Large\\frac{1}{4}[\/latex]\r\n\r\n[latex]p-\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{2}{3}[\/latex]\r\n\r\n[latex]y-\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{3}{5}[\/latex]\r\n\r\n[latex]y=\\Large\\frac{27}{20}[\/latex]\r\n\r\nSolve Equations that Need to be Simplified<\/strong>\r\nIn the following exercises, solve each equation.\r\n\r\n[latex]c+3 - 10=18[\/latex]\r\n\r\n[latex]m+6 - 8=15[\/latex]\r\n\r\n17\r\n\r\n[latex]9x+5 - 8x+14=20[\/latex]\r\n\r\n[latex]6x+8 - 5x+16=32[\/latex]\r\n\r\n8\r\n\r\n[latex]-6x - 11+7x - 5=-16[\/latex]\r\n\r\n[latex]-8n - 17+9n - 4=-41[\/latex]\r\n\r\n\u221220\r\n\r\n[latex]3\\left(y - 5\\right)-2y=-7[\/latex]\r\n\r\n[latex]4\\left(y - 2\\right)-3y=-6[\/latex]\r\n\r\n2\r\n\r\n[latex]8\\left(u+1.5\\right)-7u=4.9[\/latex]\r\n\r\n[latex]5\\left(w+2.2\\right)-4w=9.3[\/latex]\r\n\r\n1.7\r\n\r\n[latex]-5\\left(y - 2\\right)+6y=-7+4[\/latex]\r\n\r\n[latex]-8\\left(x - 1\\right)+9x=-3+9[\/latex]\r\n\r\n\u22122\r\n\r\n[latex]3\\left(5n - 1\\right)-14n+9=1 - 2[\/latex]\r\n\r\n[latex]2\\left(8m+3\\right)-15m - 4=3 - 5[\/latex]\r\n\r\n\u22124\r\n\r\n[latex]-\\left(j+2\\right)+2j - 1=5[\/latex]\r\n\r\n[latex]-\\left(k+7\\right)+2k+8=7[\/latex]\r\n\r\n6\r\n\r\n[latex]6a - 5\\left(a - 2\\right)+9=-11[\/latex]\r\n\r\n[latex]8c - 7\\left(c - 3\\right)+4=-16[\/latex]\r\n\r\n\u221241\r\n\r\n[latex]8\\left(4x+5\\right)-5\\left(6x\\right)-x=53[\/latex]\r\n\r\n[latex]6\\left(9y - 1\\right)-10\\left(5y\\right)-3y=22[\/latex]\r\n\r\n28\r\n

Translate to an Equation and Solve<\/strong><\/h3>\r\nIn the following exercises, translate to an equation and then solve.\r\n\r\nFive more than [latex]x[\/latex] is equal to [latex]21[\/latex].\r\n\r\nThe sum of [latex]x[\/latex] and [latex]-5[\/latex] is [latex]33[\/latex].\r\n\r\nx<\/em> + (\u22125) = 33; x<\/em> = 38\r\n\r\nTen less than [latex]m[\/latex] is [latex]-14[\/latex].\r\n\r\nThree less than [latex]y[\/latex] is [latex]-19[\/latex].\r\n\r\ny<\/em> \u2212 3 = \u221219; y<\/em> = \u221216\r\n\r\nThe sum of [latex]y[\/latex] and [latex]-3[\/latex] is [latex]40[\/latex].\r\n\r\nEight more than [latex]p[\/latex] is equal to [latex]52[\/latex].\r\n\r\np<\/em> + 8 = 52; p<\/em> = 44\r\n\r\nThe difference of [latex]9x[\/latex] and [latex]8x[\/latex] is [latex]17[\/latex].\r\n\r\nThe difference of [latex]5c[\/latex] and [latex]4c[\/latex] is [latex]60[\/latex].\r\n\r\n5c<\/em> \u2212 4c<\/em> = 60; 60\r\n\r\nThe difference of [latex]n[\/latex] and [latex]\\Large\\frac{1}{6}[\/latex] is [latex]\\Large\\frac{1}{2}[\/latex].\r\n\r\nThe difference of [latex]f[\/latex] and [latex]\\Large\\frac{1}{3}[\/latex] is [latex]\\Large\\frac{1}{12}[\/latex].\r\n\r\n[latex]f-\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{12}\\normalsize ;\\Large\\frac{5}{12}[\/latex]\r\n\r\nThe sum of [latex]-4n[\/latex] and [latex]5n[\/latex] is [latex]-32[\/latex].\r\n\r\nThe sum of [latex]-9m[\/latex] and [latex]10m[\/latex] is [latex]-25[\/latex].\r\n\r\n\u22129m<\/em> + 10m<\/em> = \u221225; m<\/em> = \u221225\r\n

Translate and Solve Applications<\/strong><\/h3>\r\nIn the following exercises, translate into an equation and solve.\r\n\r\nPilar drove from home to school and then to her aunt\u2019s house, a total of [latex]18[\/latex] miles. The distance from Pilar\u2019s house to school is [latex]7[\/latex] miles. What is the distance from school to her aunt\u2019s house?\r\n\r\nJeff read a total of [latex]54[\/latex] pages in his English and Psychology textbooks. He read [latex]41[\/latex] pages in his English textbook. How many pages did he read in his Psychology textbook?\r\n\r\nLet p<\/em> equal the number of pages read in the Psychology book 41 + p<\/em> = 54. Jeff read pages in his Psychology book.\r\n\r\nPablo\u2019s father is [latex]3[\/latex] years older than his mother. Pablo\u2019s mother is [latex]42[\/latex] years old. How old is his father?\r\n\r\nEva\u2019s daughter is [latex]5[\/latex] years younger than her son. Eva\u2019s son is [latex]12[\/latex] years old. How old is her daughter?\r\n\r\nLet d<\/em> equal the daughter\u2019s age. d = 12 \u2212 5. Eva\u2019s daughter\u2019s age is 7 years old.\r\n\r\nAllie weighs [latex]8[\/latex] pounds less than her twin sister Lorrie. Allie weighs [latex]124[\/latex] pounds. How much does Lorrie weigh?\r\n\r\nFor a family birthday dinner, Celeste bought a turkey that weighed [latex]5[\/latex] pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed [latex]16[\/latex] pounds. How much did the Thanksgiving turkey weigh?\r\n\r\n21 pounds\r\n\r\nThe nurse reported that Tricia\u2019s daughter had gained [latex]4.2[\/latex] pounds since her last checkup and now weighs [latex]31.6[\/latex] pounds. How much did Tricia\u2019s daughter weigh at her last checkup?\r\n\r\nConnor\u2019s temperature was [latex]0.7[\/latex] degrees higher this morning than it had been last night. His temperature this morning was [latex]101.2[\/latex] degrees. What was his temperature last night?\r\n\r\n100.5 degrees\r\n\r\nMelissa\u2019s math book cost [latex]{$22.85}[\/latex] less than her art book cost. Her math book cost [latex]{$93.75}[\/latex]. How much did her art book cost?\r\n\r\nRon\u2019s paycheck this week was [latex]{$17.43}[\/latex] less than his paycheck last week. His paycheck this week was [latex]{$103.76}[\/latex]. How much was Ron\u2019s paycheck last week?\r\n\r\n$121.19\r\n
\r\n

everyday math<\/h3>\r\n

Baking<\/strong><\/h4>\r\nKelsey needs [latex]\\Large\\frac{2}{3}[\/latex] cup of sugar for the cookie recipe she wants to make. She only has [latex]\\Large\\frac{1}{4}[\/latex] cup of sugar and will borrow the rest from her neighbor. Let [latex]s[\/latex] equal the amount of sugar she will borrow. Solve the equation [latex]\\Large\\frac{1}{4}\\normalsize +s=\\Large\\frac{2}{3}[\/latex] to find the amount of sugar she should ask to borrow.\r\n

Construction<\/strong><\/h4>\r\nMiguel wants to drill a hole for a [latex]\\Large\\frac{5}{\\text{8}}\\normalsize\\text{-inch}[\/latex] screw. The screw should be [latex]\\Large\\frac{1}{12}[\/latex] inch larger than the hole. Let [latex]d[\/latex] equal the size of the hole he should drill. Solve the equation [latex]d+\\Large\\frac{1}{12}\\normalsize =\\Large\\frac{5}{8}[\/latex] to see what size the hole should be.\r\n\r\n[latex]d=\\Large\\frac{13}{24}[\/latex]\r\n\r\n<\/div>\r\n \r\n
\r\n

writing exercises<\/h3>\r\nIs [latex]-18[\/latex] a solution to the equation [latex]3x=16 - 5x?[\/latex] How do you know?\r\n\r\nWrite a word sentence that translates the equation [latex]y - 18=41[\/latex] and then make up an application that uses this equation in its solution.\r\n\r\nAnswers will vary.\r\n\r\n<\/div>\r\n \r\n

Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\r\n

Solve Equations Using the Division and Multiplication Properties of Equality<\/strong><\/h3>\r\nIn the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.\r\n\r\n[latex]8x=32[\/latex]\r\n\r\n[latex]7p=63[\/latex]\r\n\r\n9\r\n\r\n[latex]-5c=55[\/latex]\r\n\r\n[latex]-9x=-27[\/latex]\r\n\r\n3\r\n\r\n[latex]-90=6y[\/latex]\r\n\r\n[latex]-72=12y[\/latex]\r\n\r\n\u22127\r\n\r\n[latex]-16p=-64[\/latex]\r\n\r\n[latex]-8m=-56[\/latex]\r\n\r\n7\r\n\r\n[latex]0.25z=3.25[\/latex]\r\n\r\n[latex]0.75a=11.25[\/latex]\r\n\r\n15\r\n\r\n[latex]-3x=0[\/latex]\r\n\r\n[latex]4x=0[\/latex]\r\n\r\n0\r\n\r\nIn the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.\r\n\r\n[latex]\\Large\\frac{x}{4}\\normalsize =15[\/latex]\r\n\r\n[latex]\\Large\\frac{z}{2}\\normalsize =14[\/latex]\r\n\r\n28\r\n\r\n[latex]-20=\\Large\\frac{q}{-5}[\/latex]\r\n\r\n[latex]\\Large\\frac{c}{-3}\\normalsize =-12[\/latex]\r\n\r\n36\r\n\r\n[latex]\\Large\\frac{y}{9}\\normalsize =-6[\/latex]\r\n\r\n[latex]\\Large\\frac{q}{6}\\normalsize =-8[\/latex]\r\n\r\n\u221248\r\n\r\n[latex]\\Large\\frac{m}{-12}\\normalsize =5[\/latex]\r\n\r\n[latex]-4=\\Large\\frac{p}{-20}[\/latex]\r\n\r\n80\r\n\r\n[latex]\\Large\\frac{2}{3}\\normalsize y=18[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{5}\\normalsize r=15[\/latex]\r\n\r\n25\r\n\r\n[latex]-\\Large\\frac{5}{8}\\normalsize w=40[\/latex]\r\n\r\n[latex]24=-\\Large\\frac{3}{4}\\normalsize x[\/latex]\r\n\r\n\u221232\r\n\r\n[latex]-\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{1}{10}\\normalsize a[\/latex]\r\n\r\n[latex]-\\Large\\frac{1}{3}\\normalsize q=-\\Large\\frac{5}{6}[\/latex]\r\n\r\n5\/2\r\n\r\nSolve Equations That Need to be Simplified<\/strong>\r\nIn the following exercises, solve the equation.\r\n\r\n[latex]8a+3a - 6a=-17+27[\/latex]\r\n\r\n[latex]6y - 3y+12y=-43+28[\/latex]\r\n\r\ny<\/em> = \u22121\r\n\r\n[latex]-9x - 9x+2x=50 - 2[\/latex]\r\n\r\n[latex]-5m+7m - 8m=-6+36[\/latex]\r\n\r\nm<\/em> = \u22125\r\n\r\n[latex]100 - 16=4p - 10p-p[\/latex]\r\n\r\n[latex]-18 - 7=5t - 9t - 6t[\/latex]\r\n\r\n[latex]t=\\Large\\frac{5}{2}[\/latex]\r\n\r\n[latex]\\Large\\frac{7}{8}\\normalsize n-\\Large\\frac{3}{4}\\normalsize n=9+2[\/latex]\r\n\r\n[latex]\\Large\\frac{5}{12}\\normalsize q+\\Large\\frac{1}{2}\\normalsize q=25 - 3[\/latex]\r\n\r\nq<\/em> = 24\r\n\r\n[latex]0.25d+0.10d=6 - 0.75[\/latex]\r\n\r\n[latex]0.05p - 0.01p=2+0.24[\/latex]\r\n\r\np<\/em> = 56\r\n
\r\n

Everyday math<\/h3>\r\nBalloons<\/strong> Ramona bought [latex]18[\/latex] balloons for a party. She wants to make [latex]3[\/latex] equal bunches. Find the number of balloons in each bunch, [latex]b[\/latex], by solving the equation [latex]3b=18[\/latex].\r\n\r\nTeaching<\/strong> Connie\u2019s kindergarten class has [latex]24[\/latex] children. She wants them to get into [latex]4[\/latex] equal groups. Find the number of children in each group, [latex]g[\/latex], by solving the equation [latex]4g=24[\/latex].\r\n\r\n6 children\r\n\r\nTicket price<\/strong> Daria paid [latex]{$36.25}[\/latex] for [latex]5[\/latex] children\u2019s tickets at the ice skating rink. Find the price of each ticket, [latex]p[\/latex], by solving the equation [latex]5p=36.25[\/latex].\r\n\r\nUnit price<\/strong> Nishant paid [latex]{$12.96}[\/latex] for a pack of [latex]12[\/latex] juice bottles. Find the price of each bottle, [latex]b[\/latex], by solving the equation [latex]12b=12.96[\/latex].\r\n\r\n$1.08\r\n\r\nFuel economy<\/strong> Tania\u2019s SUV gets half as many miles per gallon (mpg) as her husband\u2019s hybrid car. The SUV gets [latex]\\text{18 mpg}[\/latex]. Find the miles per gallons, [latex]m[\/latex], of the hybrid car, by solving the equation [latex]\\Large\\frac{1}{2}\\normalsize m=18[\/latex].\r\n\r\nFabric<\/strong> The drill team used [latex]14[\/latex] yards of fabric to make flags for one-third of the members. Find how much fabric, [latex]f[\/latex], they would need to make flags for the whole team by solving the equation [latex]\\Large\\frac{1}{3}\\normalsize f=14[\/latex].\r\n\r\n42 yards\r\n\r\n<\/div>\r\n \r\n
\r\n

writing exercises<\/h3>\r\nFrida started to solve the equation [latex]-3x=36[\/latex] by adding [latex]3[\/latex] to both sides. Explain why Frida\u2019s method will result in the correct solution.\r\n\r\nEmiliano thinks [latex]x=40[\/latex] is the solution to the equation [latex]\\Large\\frac{1}{2}\\normalsize x=80[\/latex]. Explain why he is wrong.\r\n\r\nAnswer will vary.\r\n

<\/h2>\r\n<\/div>\r\n

<\/h2>\r\n

Solve Equations with Variables and Constants on Both Sides<\/h2>\r\n

Solve an Equation with Constants on Both Sides<\/strong><\/h3>\r\nIn the following exercises, solve the equation for the variable.\r\n\r\n[latex]6x - 2=40[\/latex]\r\n\r\n[latex]7x - 8=34[\/latex]\r\n\r\n6\r\n\r\n[latex]11w+6=93[\/latex]\r\n\r\n[latex]14y+7=91[\/latex]\r\n\r\n6\r\n\r\n[latex]3a+8=-46[\/latex]\r\n\r\n[latex]4m+9=-23[\/latex]\r\n\r\n\u22128\r\n\r\n[latex]-50=7n - 1[\/latex]\r\n\r\n[latex]-47=6b+1[\/latex]\r\n\r\n\u22128\r\n\r\n[latex]25=-9y+7[\/latex]\r\n\r\n[latex]29=-8x - 3[\/latex]\r\n\r\n\u22124\r\n\r\n[latex]-12p - 3=15[\/latex]\r\n\r\n[latex]-14\\text{q}-15=13[\/latex]\r\n\r\n\u22122\r\n\r\nSolve an Equation with Variables on Both Sides<\/strong>\r\nIn the following exercises, solve the equation for the variable.\r\n\r\n[latex]8z=7z - 7[\/latex]\r\n\r\n[latex]9k=8k - 11[\/latex]\r\n\r\n\u221211\r\n\r\n[latex]4x+36=10x[\/latex]\r\n\r\n[latex]6x+27=9x[\/latex]\r\n\r\n9\r\n\r\n[latex]c=-3c - 20[\/latex]\r\n\r\n[latex]b=-4b - 15[\/latex]\r\n\r\n\u22123\r\n\r\n[latex]5q=44 - 6q[\/latex]\r\n\r\n[latex]7z=39 - 6z[\/latex]\r\n\r\n3\r\n\r\n[latex]3y+\\Large\\frac{1}{2}\\normalsize =2y[\/latex]\r\n\r\n[latex]8x+\\Large\\frac{3}{4}\\normalsize =7x[\/latex]\r\n\r\n\u22123\/4\r\n\r\n[latex]-12a - 8=-16a[\/latex]\r\n\r\n[latex]-15r - 8=-11r[\/latex]\r\n\r\n2\r\n\r\nSolve an Equation with Variables and Constants on Both Sides<\/strong>\r\nIn the following exercises, solve the equations for the variable.\r\n\r\n[latex]6x - 15=5x+3[\/latex]\r\n\r\n[latex]4x - 17=3x+2[\/latex]\r\n\r\n19\r\n\r\n[latex]26+8d=9d+11[\/latex]\r\n\r\n[latex]21+6f=7f+14[\/latex]\r\n\r\n7\r\n\r\n[latex]3p - 1=5p - 33[\/latex]\r\n\r\n[latex]8q - 5=5q - 20[\/latex]\r\n\r\n\u22125\r\n\r\n[latex]4a+5=-a - 40[\/latex]\r\n\r\n[latex]9c+7=-2c - 37[\/latex]\r\n\r\n\u22124\r\n\r\n[latex]8y - 30=-2y+30[\/latex]\r\n\r\n[latex]12x - 17=-3x+13[\/latex]\r\n\r\n2\r\n\r\n[latex]2\\text{z}-4=23-\\text{z}[\/latex]\r\n\r\n[latex]3y - 4=12-y[\/latex]\r\n\r\n4\r\n\r\n[latex]\\Large\\frac{5}{4}\\normalsize c - 3=\\Large\\frac{1}{4}\\normalsize c - 16[\/latex]\r\n\r\n[latex]\\Large\\frac{4}{3}\\normalsize m - 7=\\Large\\frac{1}{3}\\normalsize m - 13[\/latex]\r\n\r\n6\r\n\r\n[latex]8-\\Large\\frac{2}{5}\\normalsize q=\\Large\\frac{3}{5}\\normalsize q+6[\/latex]\r\n\r\n[latex]11-\\Large\\frac{1}{4}\\normalsize a=\\Large\\frac{3}{4}\\normalsize a+4[\/latex]\r\n\r\n7\r\n\r\n[latex]\\Large\\frac{4}{3}\\normalsize n+9=\\Large\\frac{1}{3}\\normalsize n - 9[\/latex]\r\n\r\n[latex]\\Large\\frac{5}{4}\\normalsize a+15=\\Large\\frac{3}{4}\\normalsize a - 5[\/latex]\r\n\r\n\u221240\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize y+7=\\Large\\frac{3}{4}\\normalsize y - 3[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{5}\\normalsize p+2=\\Large\\frac{4}{5}\\normalsize p - 1[\/latex]\r\n\r\n3\r\n\r\n[latex]14n+8.25=9n+19.60[\/latex]\r\n\r\n[latex]13z+6.45=8z+23.75[\/latex]\r\n\r\n3.46\r\n\r\n[latex]2.4w - 100=0.8w+28[\/latex]\r\n\r\n[latex]2.7w - 80=1.2w+10[\/latex]\r\n\r\n60\r\n\r\n[latex]5.6r+13.1=3.5r+57.2[\/latex]\r\n\r\n[latex]6.6x - 18.9=3.4x+54.7[\/latex]\r\n\r\n23\r\n\r\nSolve an Equation Using the General Strategy<\/strong>\r\nIn the following exercises, solve the linear equation using the general strategy.\r\n\r\n[latex]5\\left(x+3\\right)=75[\/latex]\r\n\r\n[latex]4\\left(y+7\\right)=64[\/latex]\r\n\r\n9\r\n\r\n[latex]8=4\\left(x - 3\\right)[\/latex]\r\n\r\n[latex]9=3\\left(x - 3\\right)[\/latex]\r\n\r\n6\r\n\r\n[latex]20\\left(y - 8\\right)=-60[\/latex]\r\n\r\n[latex]14\\left(y - 6\\right)=-42[\/latex]\r\n\r\n3\r\n\r\n[latex]-4\\left(2n+1\\right)=16[\/latex]\r\n\r\n[latex]-7\\left(3n+4\\right)=14[\/latex]\r\n\r\n\u22122\r\n\r\n[latex]3\\left(10+5r\\right)=0[\/latex]\r\n\r\n[latex]8\\left(3+3\\text{p}\\right)=0[\/latex]\r\n\r\n\u22121\r\n\r\n[latex]\\Large\\frac{2}{3}\\normalsize\\left(9c - 3\\right)=22[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{5}\\normalsize\\left(10x - 5\\right)=27[\/latex]\r\n\r\n5\r\n\r\n[latex]5\\left(1.2u - 4.8\\right)=-12[\/latex]\r\n\r\n[latex]4\\left(2.5v - 0.6\\right)=7.6[\/latex]\r\n\r\n0.52\r\n\r\n[latex]0.2\\left(30n+50\\right)=28[\/latex]\r\n\r\n[latex]0.5\\left(16m+34\\right)=-15[\/latex]\r\n\r\n0.25\r\n\r\n[latex]-\\left(w - 6\\right)=24[\/latex]\r\n\r\n[latex]-\\left(t - 8\\right)=17[\/latex]\r\n\r\n\u22129\r\n\r\n[latex]9\\left(3a+5\\right)+9=54[\/latex]\r\n\r\n[latex]8\\left(6b - 7\\right)+23=63[\/latex]\r\n\r\n2\r\n\r\n[latex]10+3\\left(z+4\\right)=19[\/latex]\r\n\r\n[latex]13+2\\left(m - 4\\right)=17[\/latex]\r\n\r\n6\r\n\r\n[latex]7+5\\left(4-q\\right)=12[\/latex]\r\n\r\n[latex]-9+6\\left(5-k\\right)=12[\/latex]\r\n\r\n3\/2\r\n\r\n[latex]15-\\left(3r+8\\right)=28[\/latex]\r\n\r\n[latex]18-\\left(9r+7\\right)=-16[\/latex]\r\n\r\n3\r\n\r\n[latex]11 - 4\\left(y - 8\\right)=43[\/latex]\r\n\r\n[latex]18 - 2\\left(y - 3\\right)=32[\/latex]\r\n\r\n\u22124\r\n\r\n[latex]9\\left(p - 1\\right)=6\\left(2p - 1\\right)[\/latex]\r\n\r\n[latex]3\\left(4n - 1\\right)-2=8n+3[\/latex]\r\n\r\n2\r\n\r\n[latex]9\\left(2m - 3\\right)-8=4m+7[\/latex]\r\n\r\n[latex]5\\left(x - 4\\right)-4x=14[\/latex]\r\n\r\n34\r\n\r\n[latex]8\\left(x - 4\\right)-7x=14[\/latex]\r\n\r\n[latex]5+6\\left(3s - 5\\right)=-3+2\\left(8s - 1\\right)[\/latex]\r\n\r\n10\r\n\r\n[latex]-12+8\\left(x - 5\\right)=-4+3\\left(5x - 2\\right)[\/latex]\r\n\r\n[latex]4\\left(x - 1\\right)-8=6\\left(3x - 2\\right)-7[\/latex]\r\n\r\n2\r\n\r\n[latex]7\\left(2x - 5\\right)=8\\left(4x - 1\\right)-9[\/latex]\r\n
\r\n

everyday math<\/h3>\r\n

Making a fence<\/strong><\/h4>\r\nJovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the width, [latex]w[\/latex], by solving the equation [latex]150=2\\left(w+15\\right)+2w[\/latex].\r\n\r\n30 feet\r\n

Concert tickets<\/strong><\/h4>\r\nAt a school concert, the total value of tickets sold was [latex]{$1,506.}[\/latex] Student tickets sold for [latex]{$6}[\/latex] and adult tickets sold for [latex]{$9.}[\/latex] The number of adult tickets sold was [latex]5[\/latex] less than [latex]3[\/latex] times the number of student tickets. Find the number of student tickets sold, [latex]s[\/latex], by solving the equation [latex]6s+9\\left(3s - 5\\right)=1506[\/latex].\r\n\r\nCoins<\/strong> Rhonda has [latex]{$1.90}[\/latex] in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, [latex]n[\/latex], by solving the equation [latex]0.05n+0.10\\left(2n - 1\\right)=1.90[\/latex].\r\n\r\n8 nickels\r\n

Fencing<\/strong><\/h4>\r\nMicah has [latex]74[\/latex] feet of fencing to make a rectangular dog pen in his yard. He wants the length to be [latex]25[\/latex] feet more than the width. Find the length, [latex]L[\/latex], by solving the equation [latex]2L+2\\left(L - 25\\right)=74[\/latex].\r\n

<\/h2>\r\n<\/div>\r\n \r\n
\r\n

writing exercises<\/h3>\r\nWhen solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?\r\n\r\nAnswers will vary.\r\n\r\nSolve the equation [latex]10x+14=-2x+38[\/latex], explaining all the steps of your solution.\r\n\r\nWhat is the first step you take when solving the equation [latex]3 - 7\\left(y - 4\\right)=38?[\/latex] Explain why this is your first step.\r\n\r\nAnswers will vary.\r\n\r\nSolve the equation [latex]\\Large\\frac{1}{4}\\normalsize\\left(8x+20\\right)=3x - 4[\/latex] explaining all the steps of your solution as in the examples in this section.\r\n\r\nUsing your own words, list the steps in the General Strategy for Solving Linear Equations.\r\n\r\nAnswers will vary.\r\n\r\nExplain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.\r\n

<\/h2>\r\n<\/div>\r\n \r\n

Solve Equations with Fraction or Decimal Coefficients<\/h2>\r\n

Solve equations with fraction coefficients<\/strong><\/h3>\r\nIn the following exercises, solve the equation by clearing the fractions.\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]\r\n\r\nx<\/em> = \u22121\r\n\r\n[latex]\\Large\\frac{3}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{1}{4}[\/latex]\r\n\r\n[latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{2}{3}\\normalsize =-\\Large\\frac{3}{2}[\/latex]\r\n\r\ny<\/em> = \u22121\r\n\r\n[latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{1}{3}\\normalsize =-\\Large\\frac{7}{6}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]a=\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]\\Large\\frac{5}{8}\\normalsize b+\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]2=\\Large\\frac{1}{3}\\normalsize x-\\Large\\frac{1}{2}\\normalsize x+\\Large\\frac{2}{3}\\normalsize x[\/latex]\r\n\r\nx<\/em> = 4\r\n\r\n[latex]2=\\Large\\frac{3}{5}\\normalsize x-\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{2}{5}\\normalsize x[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize m-\\Large\\frac{4}{5}\\normalsize m+\\Large\\frac{1}{2}\\normalsize m=-1[\/latex]\r\n\r\nm<\/em> = 20\r\n\r\n[latex]\\Large\\frac{5}{6}\\normalsize n-\\Large\\frac{1}{4}\\normalsize n-\\Large\\frac{1}{2}\\normalsize n=-2[\/latex]\r\n\r\n[latex]x+\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{2}{3}\\normalsize x-\\Large\\frac{1}{2}[\/latex]\r\n\r\nx<\/em> = \u22123\r\n\r\n[latex]x+\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{5}{4}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize w+\\Large\\frac{5}{4}\\normalsize =w-\\Large\\frac{1}{4}[\/latex]\r\n\r\n[latex]w=\\Large\\frac{9}{4}[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{2}\\normalsize z+\\Large\\frac{1}{3}\\normalsize =z-\\Large\\frac{2}{3}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{12}\\normalsize x+\\Large\\frac{1}{6}[\/latex]\r\n\r\nx<\/em> = 1\r\n\r\n[latex]\\Large\\frac{1}{2}\\normalsize a-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{6}\\normalsize a+\\Large\\frac{1}{12}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize b+\\Large\\frac{1}{5}\\normalsize =\\Large\\frac{2}{5}\\normalsize b-\\Large\\frac{3}{5}[\/latex]\r\n\r\nb<\/em> = 12\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{1}{5}\\normalsize x-\\Large\\frac{2}{5}[\/latex]\r\n\r\n[latex]1=\\Large\\frac{1}{6}\\normalsize\\left(12x - 6\\right)[\/latex]\r\n\r\nx<\/em> = 1\r\n\r\n[latex]1=\\Large\\frac{1}{5}\\normalsize\\left(15x - 10\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize\\left(p - 7\\right)=\\Large\\frac{1}{3}\\normalsize\\left(p+5\\right)[\/latex]\r\n\r\np<\/em> = \u221241\r\n\r\n[latex]\\Large\\frac{1}{5}\\normalsize\\left(q+3\\right)=\\Large\\frac{1}{2}\\normalsize\\left(q - 3\\right)[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{2}\\normalsize\\left(x+4\\right)=\\Large\\frac{3}{4}[\/latex]\r\n\r\n[latex]x=-\\Large\\frac{5}{2}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize\\left(x+5\\right)=\\Large\\frac{5}{6}[\/latex]\r\n

Solve Equations with Decimal Coefficients<\/strong><\/h3>\r\nIn the following exercises, solve the equation by clearing the decimals.\r\n\r\n[latex]0.6y+3=9[\/latex]\r\n\r\ny<\/em> = 10\r\n\r\n[latex]0.4y - 4=2[\/latex]\r\n\r\n[latex]3.6j - 2=5.2[\/latex]\r\n\r\nj<\/em> = 2\r\n\r\n[latex]2.1k+3=7.2[\/latex]\r\n\r\n[latex]0.4x+0.6=0.5x - 1.2[\/latex]\r\n\r\nx<\/em> = 18\r\n\r\n[latex]0.7x+0.4=0.6x+2.4[\/latex]\r\n\r\n[latex]0.23x+1.47=0.37x - 1.05[\/latex]\r\n\r\nx<\/em> = 18\r\n\r\n[latex]0.48x+1.56=0.58x - 0.64[\/latex]\r\n\r\n[latex]0.9x - 1.25=0.75x+1.75[\/latex]\r\n\r\nx<\/em> = 20\r\n\r\n[latex]1.2x - 0.91=0.8x+2.29[\/latex]\r\n\r\n[latex]0.05n+0.10\\left(n+8\\right)=2.15[\/latex]\r\n\r\nn<\/em> = 9\r\n\r\n[latex]0.05n+0.10\\left(n+7\\right)=3.55[\/latex]\r\n\r\n[latex]0.10d+0.25\\left(d+5\\right)=4.05[\/latex]\r\n\r\nd<\/em> = 8\r\n\r\n[latex]0.10d+0.25\\left(d+7\\right)=5.25[\/latex]\r\n\r\n[latex]0.05\\left(q - 5\\right)+0.25q=3.05[\/latex]\r\n\r\nq<\/em> = 11\r\n\r\n[latex]0.05\\left(q - 8\\right)+0.25q=4.10[\/latex]\r\n
\r\n

Everyday math<\/h3>\r\nCoins<\/strong> Taylor has [latex]{$2.00}[\/latex] in dimes and pennies. The number of pennies is [latex]2[\/latex] more than the number of dimes. Solve the equation [latex]0.10d+0.01\\left(d+2\\right)=2[\/latex] for [latex]d[\/latex], the number of dimes.\r\n\r\nd<\/em> = 18\r\n\r\nStamps<\/strong> Travis bought [latex]{$9.45}[\/latex] worth of [latex]\\text{49-cent}[\/latex] stamps and [latex]\\text{21-cent}[\/latex] stamps. The number of [latex]\\text{21-cent}[\/latex] stamps was [latex]5[\/latex] less than the number of [latex]\\text{49-cent}[\/latex] stamps. Solve the equation [latex]0.49s+0.21\\left(s - 5\\right)=9.45[\/latex] for [latex]s[\/latex], to find the number of [latex]\\text{49-cent}[\/latex] stamps Travis bought.\r\n\r\n<\/div>\r\n \r\n
\r\n

writing exercises<\/h3>\r\nExplain how to find the least common denominator of [latex]\\Large\\frac{3}{8}\\normalsize ,\\Large\\frac{1}{6}\\normalsize ,\\text{and}\\Large\\frac{2}{3}[\/latex].\r\n\r\nAnswers will vary.\r\n\r\nIf an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?\r\n\r\nIf an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?\r\n\r\nAnswers will vary.\r\n\r\nIn the equation [latex]0.35x+2.1=3.85[\/latex], what is the LCD? How do you know?\r\n

<\/h2>\r\n<\/div>\r\n \r\n

Chapter Review Exercises<\/h3>\r\n
\r\n

Solve Equations using the Subtraction and Addition Properties of Equality<\/h3>\r\nIn the following exercises, determine whether the given number is a solution to the equation.\r\n\r\n[latex]x+16=31,x=15[\/latex]\r\n\r\nyes\r\n\r\n[latex]w - 8=5,w=3[\/latex]\r\n\r\n[latex]-9n=45,n=54[\/latex]\r\n\r\nno\r\n\r\n[latex]4a=72,a=18[\/latex]\r\n\r\nIn the following exercises, solve the equation using the Subtraction Property of Equality.\r\n\r\n[latex]x+7=19[\/latex]\r\n\r\n12\r\n\r\n[latex]y+2=-6[\/latex]\r\n\r\n[latex]a+\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{5}{3}[\/latex]\r\n\r\n[latex]a=\\Large\\frac{4}{3}[\/latex]\r\n\r\n[latex]n+3.6=5.1[\/latex]\r\n\r\nIn the following exercises, solve the equation using the Addition Property of Equality.\r\n\r\n[latex]u - 7=10[\/latex]\r\n\r\nu<\/em> = 17\r\n\r\n[latex]x - 9=-4[\/latex]\r\n\r\n[latex]c-\\Large\\frac{3}{11}\\normalsize =\\Large\\frac{9}{11}[\/latex]\r\n\r\n[latex]c=\\Large\\frac{12}{11}[\/latex]\r\n\r\n[latex]p - 4.8=14[\/latex]\r\n\r\nIn the following exercises, solve the equation.\r\n\r\n[latex]n - 12=32[\/latex]\r\n\r\nn<\/em> = 44\r\n\r\n[latex]y+16=-9[\/latex]\r\n\r\n[latex]f+\\Large\\frac{2}{3}\\normalsize =4[\/latex]\r\n\r\n[latex]f=\\Large\\frac{10}{3}[\/latex]\r\n\r\n[latex]d - 3.9=8.2[\/latex]\r\n\r\n[latex]y+8 - 15=-3[\/latex]\r\n\r\ny<\/em> = 4\r\n\r\n[latex]7x+10 - 6x+3=5[\/latex]\r\n\r\n[latex]6\\left(n - 1\\right)-5n=-14[\/latex]\r\n\r\nn<\/em> = \u22128\r\n\r\n[latex]8\\left(3p+5\\right)-23\\left(p - 1\\right)=35[\/latex]\r\n\r\nIn the following exercises, translate each English sentence into an algebraic equation and then solve it.\r\n\r\nThe sum of [latex]-6[\/latex] and [latex]m[\/latex] is [latex]25[\/latex].\r\n\r\n\u22126 + m<\/em> = 25; m<\/em> = 31\r\n\r\nFour less than [latex]n[\/latex] is [latex]13[\/latex].\r\n\r\nIn the following exercises, translate into an algebraic equation and solve.\r\n\r\nRochelle\u2019s daughter is [latex]11[\/latex] years old. Her son is [latex]3[\/latex] years younger. How old is her son?\r\n\r\ns<\/em> = 11 \u2212 3; 8 years old\r\n\r\nTan weighs [latex]146[\/latex] pounds. Minh weighs [latex]15[\/latex] pounds more than Tan. How much does Minh weigh?\r\n\r\nPeter paid [latex]{$9.75}[\/latex] to go to the movies, which was [latex]{$46.25}[\/latex] less than he paid to go to a concert. How much did he pay for the concert?\r\n\r\nc<\/em> \u2212 46.25 = 9.75; $56.00\r\n\r\nElissa earned [latex]{$152.84}[\/latex] this week, which was [latex]{$21.65}[\/latex] more than she earned last week. How much did she earn last week?\r\n

<\/h2>\r\n<\/div>\r\n \r\n
\r\n

Solve Equations using the Division and Multiplication Properties of Equality<\/h3>\r\nIn the following exercises, solve each equation using the Division Property of Equality.\r\n\r\n[latex]8x=72[\/latex]\r\n\r\nx<\/em> = 9\r\n\r\n[latex]13a=-65[\/latex]\r\n\r\n[latex]0.25p=5.25[\/latex]\r\n\r\np<\/em> = 21\r\n\r\n[latex]-y=4[\/latex]\r\n\r\nIn the following exercises, solve each equation using the Multiplication Property of Equality.\r\n\r\n[latex]\\Large\\frac{n}{6}\\normalsize =18[\/latex]\r\n\r\nn<\/em> = 108\r\n\r\n[latex]\\Large\\frac{y}{-10}\\normalsize =30[\/latex]\r\n\r\n[latex]36=\\Large\\frac{3}{4}\\normalsize x[\/latex]\r\n\r\nx<\/em> = 48\r\n\r\n[latex]\\Large\\frac{5}{8}\\normalsize u=\\Large\\frac{15}{16}[\/latex]\r\n\r\nIn the following exercises, solve each equation.\r\n\r\n[latex]-18m=-72[\/latex]\r\n\r\nm<\/em> = 4\r\n\r\n[latex]\\Large\\frac{c}{9}\\normalsize =36[\/latex]\r\n\r\n[latex]0.45x=6.75[\/latex]\r\n\r\nx<\/em> = 15\r\n\r\n[latex]\\Large\\frac{11}{12}\\normalsize =\\Large\\frac{2}{3}\\normalsize y[\/latex]\r\n\r\n[latex]5r - 3r+9r=35 - 2[\/latex]\r\n\r\nr<\/em> = 3\r\n\r\n[latex]24x+8x - 11x=-7 - 14[\/latex]\r\n

<\/h2>\r\n<\/div>\r\n \r\n
\r\n

Solve Equations with Variables and Constants on Both Sides<\/h3>\r\nIn the following exercises, solve the equations with constants on both sides.\r\n\r\n[latex]8p+7=47[\/latex]\r\n\r\np<\/em> = 5\r\n\r\n[latex]10w - 5=65[\/latex]\r\n\r\n[latex]3x+19=-47[\/latex]\r\n\r\nx<\/em> = \u221222\r\n\r\n[latex]32=-4 - 9n[\/latex]\r\n\r\nIn the following exercises, solve the equations with variables on both sides.\r\n\r\n[latex]7y=6y - 13[\/latex]\r\n\r\ny<\/em> = \u221213\r\n\r\n[latex]5a+21=2a[\/latex]\r\n\r\n[latex]k=-6k - 35[\/latex]\r\n\r\nk<\/em> = \u22125\r\n\r\n[latex]4x-\\Large\\frac{3}{8}\\normalsize =3x[\/latex]\r\n\r\nIn the following exercises, solve the equations with constants and variables on both sides.\r\n\r\n[latex]12x - 9=3x+45[\/latex]\r\n\r\nx<\/em> = 6\r\n\r\n[latex]5n - 20=-7n - 80[\/latex]\r\n\r\n[latex]4u+16=-19-u[\/latex]\r\n\r\nu<\/em> = \u22127\r\n\r\n[latex]\\Large\\frac{5}{8}\\normalsize c - 4=\\Large\\frac{3}{8}\\normalsize c+4[\/latex]\r\n\r\nIn the following exercises, solve each linear equation using the general strategy.\r\n\r\n[latex]6\\left(x+6\\right)=24[\/latex]\r\n\r\nx<\/em> = \u22122\r\n\r\n[latex]9\\left(2p - 5\\right)=72[\/latex]\r\n\r\n[latex]-\\left(s+4\\right)=18[\/latex]\r\n\r\ns<\/em> = \u221222\r\n\r\n[latex]8+3\\left(n - 9\\right)=17[\/latex]\r\n\r\n[latex]23 - 3\\left(y - 7\\right)=8[\/latex]\r\n\r\ny<\/em> = 12\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize\\left(6m+21\\right)=m - 7[\/latex]\r\n\r\n[latex]8\\left(r - 2\\right)=6\\left(r+10\\right)[\/latex]\r\n\r\nr<\/em> = 38\r\n\r\n[latex]5+7\\left(2 - 5x\\right)=2\\left(9x+1\\right)-\\left(13x - 57\\right)[\/latex]\r\n\r\n[latex]4\\left(3.5y+0.25\\right)=365[\/latex]\r\n\r\ny<\/em> = 26\r\n\r\n[latex]0.25\\left(q - 8\\right)=0.1\\left(q+7\\right)[\/latex]\r\n

<\/h2>\r\n<\/div>\r\n \r\n
\r\n

Solve Equations with Fraction or Decimal Coefficients<\/h3>\r\nIn the following exercises, solve each equation by clearing the fractions.\r\n\r\n[latex]\\Large\\frac{2}{5}\\normalsize n-\\Large\\frac{1}{10}\\normalsize =\\Large\\frac{7}{10}[\/latex]\r\n\r\nn<\/em> = 2\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{1}{5}\\normalsize x=8[\/latex]\r\n\r\n[latex]\\Large\\frac{3}{4}\\normalsize a-\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{5}{6}[\/latex]\r\n\r\n[latex]a=\\Large\\frac{14}{3}[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{2}\\normalsize\\left(k+3\\right)=\\Large\\frac{1}{3}\\normalsize\\left(k+16\\right)[\/latex]\r\n\r\nIn the following exercises, solve each equation by clearing the decimals.\r\n\r\n[latex]0.8x - 0.3=0.7x+0.2[\/latex]\r\n\r\nx<\/em> = 5\r\n\r\n[latex]0.36u+2.55=0.41u+6.8[\/latex]\r\n\r\n[latex]0.6p - 1.9=0.78p+1.7[\/latex]\r\n\r\np<\/em> = \u221220\r\n\r\n[latex]0.10d+0.05\\left(d - 4\\right)=2.05[\/latex]\r\n

<\/h1>\r\n<\/div>\r\n \r\n
\r\n

Chapter Practice Test<\/h3>\r\nDetermine whether each number is a solution to the equation.\r\n\r\n[latex]3x+5=23[\/latex].\r\n\r\n\u24d0 [latex]6[\/latex]\r\n\u24d1 [latex]\\Large\\frac{23}{5}[\/latex]\r\n\r\n\u24d0 yes\r\n\u24d1 no\r\n\r\nIn the following exercises, solve each equation.\r\n\r\n[latex]n - 18=31[\/latex]\r\n\r\n[latex]9c=144[\/latex]\r\n\r\nc<\/em> = 16\r\n\r\n[latex]4y - 8=16[\/latex]\r\n\r\n[latex]-8x - 15+9x - 1=-21[\/latex]\r\n\r\nx<\/em> = \u22125\r\n\r\n[latex]-15a=120[\/latex]\r\n\r\n[latex]\\Large\\frac{2}{3}\\normalsize x=6[\/latex]\r\n\r\nx<\/em> = 9\r\n\r\n[latex]x+3.8=8.2[\/latex]\r\n\r\n[latex]10y=-5y+60[\/latex]\r\n\r\ny<\/em> = 4\r\n\r\n[latex]8n+2=6n+12[\/latex]\r\n\r\n[latex]9m - 2 - 4m+m=42 - 8[\/latex]\r\n\r\nm<\/em> = 6\r\n\r\n[latex]-5\\left(2x+1\\right)=45[\/latex]\r\n\r\n[latex]-\\left(d+9\\right)=23[\/latex]\r\n\r\nd<\/em> = \u221232\r\n\r\n[latex]\\Large\\frac{1}{3}\\normalsize\\left(6m+21\\right)=m - 7[\/latex]\r\n\r\n[latex]2\\left(6x+5\\right)-8=-22[\/latex]\r\n\r\nx<\/em> = \u22122\r\n\r\n[latex]8\\left(3a+5\\right)-7\\left(4a - 3\\right)=20 - 3a[\/latex]\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize p+\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{2}[\/latex]\r\n\r\n[latex]p=\\Large\\frac{2}{3}[\/latex]\r\n\r\n[latex]0.1d+0.25\\left(d+8\\right)=4.1[\/latex]\r\n\r\nTranslate and solve: The difference of twice [latex]x[\/latex] and [latex]4[\/latex] is [latex]16[\/latex].\r\n\r\n2x<\/em> \u2212 4 = 16; x<\/em> = 10\r\n\r\nSamuel paid [latex]{$25.82}[\/latex] for gas this week, which was [latex]{$3.47}[\/latex] less than he paid last week. How much did he pay last week?\r\n

Determine Whether a Decimal is a Solution of an Equation<\/b>\r\nIn the following exercises, determine whether each number is a solution of the given equation.<\/span><\/p>\r\n

[latex]x - 0.8=2.3[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> [latex]x=2[\/latex] <\/span>\u24d1<\/span> [latex]x=-1.5[\/latex] <\/span>\u24d2<\/span> [latex]x=3.1[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> no\r\n<\/span>\u24d1<\/span> no\r\n<\/span>\u24d2<\/span> yes<\/span><\/p>\r\n

[latex]y+0.6=-3.4[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> [latex]y=-4[\/latex] <\/span>\u24d1<\/span> [latex]y=-2.8[\/latex] <\/span>\u24d2<\/span> [latex]y=2.6[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{h}{1.5}\\normalsize =-4.3[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> [latex]h=6.45[\/latex] <\/span>\u24d1<\/span> [latex]h=-6.45[\/latex] <\/span>\u24d2<\/span> [latex]h=-2.1[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> no\r\n<\/span>\u24d1<\/span> yes\r\n<\/span>\u24d2<\/span> no<\/span><\/p>\r\n

[latex]0.75k=-3.6[\/latex]<\/span><\/p>\r\n

\u24d0<\/span> [latex]k=-0.48[\/latex] <\/span>\u24d1<\/span> [latex]k=-4.8[\/latex] <\/span>\u24d2<\/span> [latex]k=-2.7[\/latex]<\/span><\/p>\r\n\r\n

Solve Equations with Decimals<\/b>\r\n<\/span><\/h4>\r\n

In the following exercises, solve the equation.<\/span><\/p>\r\n

[latex]y+2.9=5.7[\/latex]<\/span><\/p>\r\n

y<\/i> = 2.8<\/span><\/p>\r\n

[latex]m+4.6=6.5[\/latex]<\/span><\/p>\r\n

[latex]f+3.45=2.6[\/latex]<\/span><\/p>\r\n

f<\/i> = \u22120.85<\/span><\/p>\r\n

[latex]h+4.37=3.5[\/latex]<\/span><\/p>\r\n

[latex]a+6.2=-1.7[\/latex]<\/span><\/p>\r\n

a<\/i> = \u22127.9<\/span><\/p>\r\n

[latex]b+5.8=-2.3[\/latex]<\/span><\/p>\r\n

[latex]c+1.15=-3.5[\/latex]<\/span><\/p>\r\n

c<\/i> = \u22124.65<\/span><\/p>\r\n

[latex]d+2.35=-4.8[\/latex]<\/span><\/p>\r\n

[latex]n - 2.6=1.8[\/latex]<\/span><\/p>\r\n

n<\/i> = 4.4<\/span><\/p>\r\n

[latex]p - 3.6=1.7[\/latex]<\/span><\/p>\r\n

[latex]x - 0.4=-3.9[\/latex]<\/span><\/p>\r\n

x<\/i> = \u22123.5<\/span><\/p>\r\n

[latex]y - 0.6=-4.5[\/latex]<\/span><\/p>\r\n

[latex]j - 1.82=-6.5[\/latex]<\/span><\/p>\r\n

j<\/i> = \u22124.68<\/span><\/p>\r\n

[latex]k - 3.19=-4.6[\/latex]<\/span><\/p>\r\n

[latex]m - 0.25=-1.67[\/latex]<\/span><\/p>\r\n

m<\/i> = \u22121.42<\/span><\/p>\r\n

[latex]q - 0.47=-1.53[\/latex]<\/span><\/p>\r\n

[latex]0.5x=3.5[\/latex]<\/span><\/p>\r\n

x<\/i> = 7<\/span><\/p>\r\n

[latex]0.4p=9.2[\/latex]<\/span><\/p>\r\n

[latex]-1.7c=8.5[\/latex]<\/span><\/p>\r\n

c<\/i> = \u22125<\/span><\/p>\r\n

[latex]-2.9x=5.8[\/latex]<\/span><\/p>\r\n

[latex]-1.4p=-4.2[\/latex]<\/span><\/p>\r\n

p<\/i> = 3<\/span><\/p>\r\n

[latex]-2.8m=-8.4[\/latex]<\/span><\/p>\r\n

[latex]-120=1.5q[\/latex]<\/span><\/p>\r\n

q<\/i> = \u221280<\/span><\/p>\r\n

[latex]-75=1.5y[\/latex]<\/span><\/p>\r\n

[latex]0.24x=4.8[\/latex]<\/span><\/p>\r\n

x<\/i> = 20<\/span><\/p>\r\n

[latex]0.18n=5.4[\/latex]<\/span><\/p>\r\n

[latex]-3.4z=-9.18[\/latex]<\/span><\/p>\r\n

z<\/i> = 2.7<\/span><\/p>\r\n

[latex]-2.7u=-9.72[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{a}{0.4}\\normalsize =-20[\/latex]<\/span><\/p>\r\n

a<\/i> = \u22128<\/span><\/p>\r\n

[latex]\\Large\\frac{b}{0.3}\\normalsize =-9[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{x}{0.7}\\normalsize =-0.4[\/latex]<\/span><\/p>\r\n

x<\/i> = \u22120.28<\/span><\/p>\r\n

[latex]\\Large\\frac{y}{0.8}\\normalsize =-0.7[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{p}{-5}\\normalsize =-1.65[\/latex]<\/span><\/p>\r\n

p<\/i> = 8.25<\/span><\/p>\r\n

[latex]\\Large\\frac{q}{-4}\\normalsize =-5.92[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{r}{-1.2}\\normalsize =-6[\/latex]<\/span><\/p>\r\n

r<\/i> = 7.2<\/span><\/p>\r\n

[latex]\\Large\\frac{s}{-1.5}\\normalsize =-3[\/latex]<\/span><\/p>\r\n\r\n

Mixed Practice<\/b>\r\n<\/span><\/h4>\r\n

In the following exercises, solve the equation. Then check your solution.<\/span><\/p>\r\n

[latex]x - 5=-11[\/latex]<\/span><\/p>\r\n

x<\/i> = \u22126<\/span><\/p>\r\n

[latex]-\\Large\\frac{2}{5}\\normalsize =x+\\Large\\frac{3}{4}[\/latex]<\/span><\/p>\r\n

[latex]p+8=-2[\/latex]<\/span><\/p>\r\n

p<\/i> = \u221210<\/span><\/p>\r\n

[latex]p+\\Large\\frac{2}{3}\\normalsize =\\Large\\frac{1}{12}[\/latex]<\/span><\/p>\r\n

[latex]-4.2m=-33.6[\/latex]<\/span><\/p>\r\n

m<\/i> = 8<\/span><\/p>\r\n

[latex]q+9.5=-14[\/latex]<\/span><\/p>\r\n

[latex]q+\\Large\\frac{5}{6}\\normalsize =\\Large\\frac{1}{12}[\/latex]<\/span><\/p>\r\n

[latex]q=-\\Large\\frac{3}{4}[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{8.6}{15}\\normalsize =-d[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{7}{8}\\normalsize m=\\Large\\frac{1}{10}[\/latex]<\/span><\/p>\r\n

[latex]m=\\Large\\frac{4}{35}[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{j}{-6.2}\\normalsize =-3[\/latex]<\/span><\/p>\r\n

[latex]-\\Large\\frac{2}{3}\\normalsize =y+\\Large\\frac{3}{8}[\/latex]<\/span><\/p>\r\n

[latex]y=-\\Large\\frac{25}{24}[\/latex]<\/span><\/p>\r\n

[latex]s - 1.75=-3.2[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{11}{20}\\normalsize =-f[\/latex]<\/span><\/p>\r\n

[latex]f=-\\Large\\frac{11}{20}[\/latex]<\/span><\/p>\r\n

[latex]-3.6b=2.52[\/latex]<\/span><\/p>\r\n

[latex]-4.2a=3.36[\/latex]<\/span><\/p>\r\n

a<\/i> = \u22120.8<\/span><\/p>\r\n

[latex]-9.1n=-63.7[\/latex]<\/span><\/p>\r\n

[latex]r - 1.25=-2.7[\/latex]<\/span><\/p>\r\n

r<\/i> = \u22121.45<\/span><\/p>\r\n

[latex]\\Large\\frac{1}{4}\\normalsize n=\\Large\\frac{7}{10}[\/latex]<\/span><\/p>\r\n

[latex]\\Large\\frac{h}{-3}\\normalsize =-8[\/latex]<\/span><\/p>\r\n

h<\/i> = 24<\/span><\/p>\r\n

[latex]y - 7.82=-16[\/latex]<\/span><\/p>\r\n\r\n

Translate to an Equation and Solve<\/b>\r\n<\/span><\/h4>\r\n

In the following exercises, translate and solve.<\/span><\/p>\r\n

The difference of [latex]n[\/latex] and [latex]1.9[\/latex] is [latex]3.4[\/latex].<\/span><\/p>\r\n

[latex]n - 1.9=3.4;5.3[\/latex]<\/span><\/p>\r\n

The difference [latex]n[\/latex] and [latex]1.5[\/latex] is [latex]0.8[\/latex].<\/span><\/p>\r\n

The product of [latex]-6.2[\/latex] and [latex]x[\/latex] is [latex]-4.96[\/latex].<\/span><\/p>\r\n

\u22126.2x<\/i> = \u22124.96; 0.8<\/span><\/p>\r\n

The product of [latex]-4.6[\/latex] and [latex]x[\/latex] is [latex]-3.22[\/latex].<\/span><\/p>\r\n

The quotient of [latex]y[\/latex] and [latex]-1.7[\/latex] is [latex]-5[\/latex].<\/span><\/p>\r\n

[latex]\\Large\\frac{y}{-1.7}\\normalsize =-5;8.5[\/latex]<\/span><\/p>\r\n

The quotient of [latex]z[\/latex] and [latex]-3.6[\/latex] is [latex]3[\/latex].<\/span><\/p>\r\n

The sum of [latex]n[\/latex] and [latex]-7.3[\/latex] is [latex]2.4[\/latex].<\/span><\/p>\r\n

n<\/i> + (\u22127.3) = 2.4; 9.7<\/span><\/p>\r\n

The sum of [latex]n[\/latex] and [latex]-5.1[\/latex] is [latex]3.8[\/latex].<\/span><\/p>\r\n\r\n

<\/h2>\r\n<\/div>\r\n

<\/h3>\r\n
\r\n

Everyday math<\/h3>\r\n

Shawn bought a pair of shoes on sale for [latex]$78[\/latex] . Solve the equation [latex]0.75p=78[\/latex] to find the original price of the shoes, [latex]p[\/latex].<\/span><\/p>\r\n

$104<\/span><\/p>\r\n

Mary bought a new refrigerator. The total price including sales tax was [latex]{$1,350}[\/latex]. Find the retail price, [latex]r[\/latex], of the refrigerator before tax by solving the equation [latex]1.08r=1,350[\/latex].<\/span><\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

writing exercises<\/h3>\r\n

Think about solving the equation [latex]1.2y=60[\/latex], but do not actually solve it. Do you think the solution should be greater than [latex]60[\/latex] or less than [latex]60?[\/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.<\/span><\/p>\r\n

Answers will vary.<\/span><\/p>\r\n

Think about solving the equation [latex]0.8x=200[\/latex], but do not actually solve it. Do you think the solution should be greater than [latex]200[\/latex] or less than [latex]200?[\/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.<\/span><\/p>\r\n\r\n<\/div>\r\n \r\n

<\/p>","rendered":"

THIS IS OPTIONAL ADDITIONAL PRACTICE<\/h3>\n

Solve Equations Using the Subtraction and Addition Properties of Equality<\/h2>\n

In the following exercises, determine whether the given value is a solution to the equation.<\/p>\n

Is [latex]y=\\Large\\frac{1}{3}[\/latex] a solution of [latex]4y+2=10y?[\/latex]<\/p>\n

yes<\/p>\n

Is [latex]x=\\Large\\frac{3}{4}[\/latex] a solution of [latex]5x+3=9x?[\/latex]<\/p>\n

Is [latex]u=-\\Large\\frac{1}{2}[\/latex] a solution of [latex]8u - 1=6u?[\/latex]<\/p>\n

no<\/p>\n

Is [latex]v=-\\Large\\frac{1}{3}[\/latex] a solution of [latex]9v - 2=3v?[\/latex]<\/p>\n

In the following exercises, solve each equation.<\/p>\n

[latex]x+7=12[\/latex]<\/p>\n

x<\/em> = 5<\/p>\n

[latex]y+5=-6[\/latex]<\/p>\n

[latex]b+\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{3}{4}[\/latex]<\/p>\n

[latex]b=\\Large\\frac{1}{2}[\/latex]<\/p>\n

[latex]a+\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{4}{5}[\/latex]<\/p>\n

[latex]p+2.4=-9.3[\/latex]<\/p>\n

p<\/em> = \u221211.7<\/p>\n

[latex]m+7.9=11.6[\/latex]<\/p>\n

[latex]a - 3=7[\/latex]<\/p>\n

a<\/em> = 10<\/p>\n

[latex]m - 8=-20[\/latex]<\/p>\n

[latex]x-\\Large\\frac{1}{3}\\normalsize=2[\/latex]<\/p>\n

[latex]x=\\Large\\frac{7}{3}[\/latex]<\/p>\n

[latex]x-\\Large\\frac{1}{5}\\normalsize =4[\/latex]<\/p>\n

[latex]y - 3.8=10[\/latex]<\/p>\n

y<\/em> = 13.8<\/p>\n

[latex]y - 7.2=5[\/latex]<\/p>\n

[latex]x - 15=-42[\/latex]<\/p>\n

x<\/em> = \u221227<\/p>\n

[latex]z+5.2=-8.5[\/latex]<\/p>\n

[latex]q+\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/p>\n

[latex]q=-\\Large\\frac{1}{4}[\/latex]<\/p>\n

[latex]p-\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{2}{3}[\/latex]<\/p>\n

[latex]y-\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{3}{5}[\/latex]<\/p>\n

[latex]y=\\Large\\frac{27}{20}[\/latex]<\/p>\n

Solve Equations that Need to be Simplified<\/strong>
\nIn the following exercises, solve each equation.<\/p>\n

[latex]c+3 - 10=18[\/latex]<\/p>\n

[latex]m+6 - 8=15[\/latex]<\/p>\n

17<\/p>\n

[latex]9x+5 - 8x+14=20[\/latex]<\/p>\n

[latex]6x+8 - 5x+16=32[\/latex]<\/p>\n

8<\/p>\n

[latex]-6x - 11+7x - 5=-16[\/latex]<\/p>\n

[latex]-8n - 17+9n - 4=-41[\/latex]<\/p>\n

\u221220<\/p>\n

[latex]3\\left(y - 5\\right)-2y=-7[\/latex]<\/p>\n

[latex]4\\left(y - 2\\right)-3y=-6[\/latex]<\/p>\n

2<\/p>\n

[latex]8\\left(u+1.5\\right)-7u=4.9[\/latex]<\/p>\n

[latex]5\\left(w+2.2\\right)-4w=9.3[\/latex]<\/p>\n

1.7<\/p>\n

[latex]-5\\left(y - 2\\right)+6y=-7+4[\/latex]<\/p>\n

[latex]-8\\left(x - 1\\right)+9x=-3+9[\/latex]<\/p>\n

\u22122<\/p>\n

[latex]3\\left(5n - 1\\right)-14n+9=1 - 2[\/latex]<\/p>\n

[latex]2\\left(8m+3\\right)-15m - 4=3 - 5[\/latex]<\/p>\n

\u22124<\/p>\n

[latex]-\\left(j+2\\right)+2j - 1=5[\/latex]<\/p>\n

[latex]-\\left(k+7\\right)+2k+8=7[\/latex]<\/p>\n

6<\/p>\n

[latex]6a - 5\\left(a - 2\\right)+9=-11[\/latex]<\/p>\n

[latex]8c - 7\\left(c - 3\\right)+4=-16[\/latex]<\/p>\n

\u221241<\/p>\n

[latex]8\\left(4x+5\\right)-5\\left(6x\\right)-x=53[\/latex]<\/p>\n

[latex]6\\left(9y - 1\\right)-10\\left(5y\\right)-3y=22[\/latex]<\/p>\n

28<\/p>\n

Translate to an Equation and Solve<\/strong><\/h3>\n

In the following exercises, translate to an equation and then solve.<\/p>\n

Five more than [latex]x[\/latex] is equal to [latex]21[\/latex].<\/p>\n

The sum of [latex]x[\/latex] and [latex]-5[\/latex] is [latex]33[\/latex].<\/p>\n

x<\/em> + (\u22125) = 33; x<\/em> = 38<\/p>\n

Ten less than [latex]m[\/latex] is [latex]-14[\/latex].<\/p>\n

Three less than [latex]y[\/latex] is [latex]-19[\/latex].<\/p>\n

y<\/em> \u2212 3 = \u221219; y<\/em> = \u221216<\/p>\n

The sum of [latex]y[\/latex] and [latex]-3[\/latex] is [latex]40[\/latex].<\/p>\n

Eight more than [latex]p[\/latex] is equal to [latex]52[\/latex].<\/p>\n

p<\/em> + 8 = 52; p<\/em> = 44<\/p>\n

The difference of [latex]9x[\/latex] and [latex]8x[\/latex] is [latex]17[\/latex].<\/p>\n

The difference of [latex]5c[\/latex] and [latex]4c[\/latex] is [latex]60[\/latex].<\/p>\n

5c<\/em> \u2212 4c<\/em> = 60; 60<\/p>\n

The difference of [latex]n[\/latex] and [latex]\\Large\\frac{1}{6}[\/latex] is [latex]\\Large\\frac{1}{2}[\/latex].<\/p>\n

The difference of [latex]f[\/latex] and [latex]\\Large\\frac{1}{3}[\/latex] is [latex]\\Large\\frac{1}{12}[\/latex].<\/p>\n

[latex]f-\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{12}\\normalsize ;\\Large\\frac{5}{12}[\/latex]<\/p>\n

The sum of [latex]-4n[\/latex] and [latex]5n[\/latex] is [latex]-32[\/latex].<\/p>\n

The sum of [latex]-9m[\/latex] and [latex]10m[\/latex] is [latex]-25[\/latex].<\/p>\n

\u22129m<\/em> + 10m<\/em> = \u221225; m<\/em> = \u221225<\/p>\n

Translate and Solve Applications<\/strong><\/h3>\n

In the following exercises, translate into an equation and solve.<\/p>\n

Pilar drove from home to school and then to her aunt\u2019s house, a total of [latex]18[\/latex] miles. The distance from Pilar\u2019s house to school is [latex]7[\/latex] miles. What is the distance from school to her aunt\u2019s house?<\/p>\n

Jeff read a total of [latex]54[\/latex] pages in his English and Psychology textbooks. He read [latex]41[\/latex] pages in his English textbook. How many pages did he read in his Psychology textbook?<\/p>\n

Let p<\/em> equal the number of pages read in the Psychology book 41 + p<\/em> = 54. Jeff read pages in his Psychology book.<\/p>\n

Pablo\u2019s father is [latex]3[\/latex] years older than his mother. Pablo\u2019s mother is [latex]42[\/latex] years old. How old is his father?<\/p>\n

Eva\u2019s daughter is [latex]5[\/latex] years younger than her son. Eva\u2019s son is [latex]12[\/latex] years old. How old is her daughter?<\/p>\n

Let d<\/em> equal the daughter\u2019s age. d = 12 \u2212 5. Eva\u2019s daughter\u2019s age is 7 years old.<\/p>\n

Allie weighs [latex]8[\/latex] pounds less than her twin sister Lorrie. Allie weighs [latex]124[\/latex] pounds. How much does Lorrie weigh?<\/p>\n

For a family birthday dinner, Celeste bought a turkey that weighed [latex]5[\/latex] pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed [latex]16[\/latex] pounds. How much did the Thanksgiving turkey weigh?<\/p>\n

21 pounds<\/p>\n

The nurse reported that Tricia\u2019s daughter had gained [latex]4.2[\/latex] pounds since her last checkup and now weighs [latex]31.6[\/latex] pounds. How much did Tricia\u2019s daughter weigh at her last checkup?<\/p>\n

Connor\u2019s temperature was [latex]0.7[\/latex] degrees higher this morning than it had been last night. His temperature this morning was [latex]101.2[\/latex] degrees. What was his temperature last night?<\/p>\n

100.5 degrees<\/p>\n

Melissa\u2019s math book cost [latex]{$22.85}[\/latex] less than her art book cost. Her math book cost [latex]{$93.75}[\/latex]. How much did her art book cost?<\/p>\n

Ron\u2019s paycheck this week was [latex]{$17.43}[\/latex] less than his paycheck last week. His paycheck this week was [latex]{$103.76}[\/latex]. How much was Ron\u2019s paycheck last week?<\/p>\n

$121.19<\/p>\n

\n

everyday math<\/h3>\n

Baking<\/strong><\/h4>\n

Kelsey needs [latex]\\Large\\frac{2}{3}[\/latex] cup of sugar for the cookie recipe she wants to make. She only has [latex]\\Large\\frac{1}{4}[\/latex] cup of sugar and will borrow the rest from her neighbor. Let [latex]s[\/latex] equal the amount of sugar she will borrow. Solve the equation [latex]\\Large\\frac{1}{4}\\normalsize +s=\\Large\\frac{2}{3}[\/latex] to find the amount of sugar she should ask to borrow.<\/p>\n

Construction<\/strong><\/h4>\n

Miguel wants to drill a hole for a [latex]\\Large\\frac{5}{\\text{8}}\\normalsize\\text{-inch}[\/latex] screw. The screw should be [latex]\\Large\\frac{1}{12}[\/latex] inch larger than the hole. Let [latex]d[\/latex] equal the size of the hole he should drill. Solve the equation [latex]d+\\Large\\frac{1}{12}\\normalsize =\\Large\\frac{5}{8}[\/latex] to see what size the hole should be.<\/p>\n

[latex]d=\\Large\\frac{13}{24}[\/latex]<\/p>\n<\/div>\n

 <\/p>\n

\n

writing exercises<\/h3>\n

Is [latex]-18[\/latex] a solution to the equation [latex]3x=16 - 5x?[\/latex] How do you know?<\/p>\n

Write a word sentence that translates the equation [latex]y - 18=41[\/latex] and then make up an application that uses this equation in its solution.<\/p>\n

Answers will vary.<\/p>\n<\/div>\n

 <\/p>\n

Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\n

Solve Equations Using the Division and Multiplication Properties of Equality<\/strong><\/h3>\n

In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.<\/p>\n

[latex]8x=32[\/latex]<\/p>\n

[latex]7p=63[\/latex]<\/p>\n

9<\/p>\n

[latex]-5c=55[\/latex]<\/p>\n

[latex]-9x=-27[\/latex]<\/p>\n

3<\/p>\n

[latex]-90=6y[\/latex]<\/p>\n

[latex]-72=12y[\/latex]<\/p>\n

\u22127<\/p>\n

[latex]-16p=-64[\/latex]<\/p>\n

[latex]-8m=-56[\/latex]<\/p>\n

7<\/p>\n

[latex]0.25z=3.25[\/latex]<\/p>\n

[latex]0.75a=11.25[\/latex]<\/p>\n

15<\/p>\n

[latex]-3x=0[\/latex]<\/p>\n

[latex]4x=0[\/latex]<\/p>\n

0<\/p>\n

In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.<\/p>\n

[latex]\\Large\\frac{x}{4}\\normalsize =15[\/latex]<\/p>\n

[latex]\\Large\\frac{z}{2}\\normalsize =14[\/latex]<\/p>\n

28<\/p>\n

[latex]-20=\\Large\\frac{q}{-5}[\/latex]<\/p>\n

[latex]\\Large\\frac{c}{-3}\\normalsize =-12[\/latex]<\/p>\n

36<\/p>\n

[latex]\\Large\\frac{y}{9}\\normalsize =-6[\/latex]<\/p>\n

[latex]\\Large\\frac{q}{6}\\normalsize =-8[\/latex]<\/p>\n

\u221248<\/p>\n

[latex]\\Large\\frac{m}{-12}\\normalsize =5[\/latex]<\/p>\n

[latex]-4=\\Large\\frac{p}{-20}[\/latex]<\/p>\n

80<\/p>\n

[latex]\\Large\\frac{2}{3}\\normalsize y=18[\/latex]<\/p>\n

[latex]\\Large\\frac{3}{5}\\normalsize r=15[\/latex]<\/p>\n

25<\/p>\n

[latex]-\\Large\\frac{5}{8}\\normalsize w=40[\/latex]<\/p>\n

[latex]24=-\\Large\\frac{3}{4}\\normalsize x[\/latex]<\/p>\n

\u221232<\/p>\n

[latex]-\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{1}{10}\\normalsize a[\/latex]<\/p>\n

[latex]-\\Large\\frac{1}{3}\\normalsize q=-\\Large\\frac{5}{6}[\/latex]<\/p>\n

5\/2<\/p>\n

Solve Equations That Need to be Simplified<\/strong>
\nIn the following exercises, solve the equation.<\/p>\n

[latex]8a+3a - 6a=-17+27[\/latex]<\/p>\n

[latex]6y - 3y+12y=-43+28[\/latex]<\/p>\n

y<\/em> = \u22121<\/p>\n

[latex]-9x - 9x+2x=50 - 2[\/latex]<\/p>\n

[latex]-5m+7m - 8m=-6+36[\/latex]<\/p>\n

m<\/em> = \u22125<\/p>\n

[latex]100 - 16=4p - 10p-p[\/latex]<\/p>\n

[latex]-18 - 7=5t - 9t - 6t[\/latex]<\/p>\n

[latex]t=\\Large\\frac{5}{2}[\/latex]<\/p>\n

[latex]\\Large\\frac{7}{8}\\normalsize n-\\Large\\frac{3}{4}\\normalsize n=9+2[\/latex]<\/p>\n

[latex]\\Large\\frac{5}{12}\\normalsize q+\\Large\\frac{1}{2}\\normalsize q=25 - 3[\/latex]<\/p>\n

q<\/em> = 24<\/p>\n

[latex]0.25d+0.10d=6 - 0.75[\/latex]<\/p>\n

[latex]0.05p - 0.01p=2+0.24[\/latex]<\/p>\n

p<\/em> = 56<\/p>\n

\n

Everyday math<\/h3>\n

Balloons<\/strong> Ramona bought [latex]18[\/latex] balloons for a party. She wants to make [latex]3[\/latex] equal bunches. Find the number of balloons in each bunch, [latex]b[\/latex], by solving the equation [latex]3b=18[\/latex].<\/p>\n

Teaching<\/strong> Connie\u2019s kindergarten class has [latex]24[\/latex] children. She wants them to get into [latex]4[\/latex] equal groups. Find the number of children in each group, [latex]g[\/latex], by solving the equation [latex]4g=24[\/latex].<\/p>\n

6 children<\/p>\n

Ticket price<\/strong> Daria paid [latex]{$36.25}[\/latex] for [latex]5[\/latex] children\u2019s tickets at the ice skating rink. Find the price of each ticket, [latex]p[\/latex], by solving the equation [latex]5p=36.25[\/latex].<\/p>\n

Unit price<\/strong> Nishant paid [latex]{$12.96}[\/latex] for a pack of [latex]12[\/latex] juice bottles. Find the price of each bottle, [latex]b[\/latex], by solving the equation [latex]12b=12.96[\/latex].<\/p>\n

$1.08<\/p>\n

Fuel economy<\/strong> Tania\u2019s SUV gets half as many miles per gallon (mpg) as her husband\u2019s hybrid car. The SUV gets [latex]\\text{18 mpg}[\/latex]. Find the miles per gallons, [latex]m[\/latex], of the hybrid car, by solving the equation [latex]\\Large\\frac{1}{2}\\normalsize m=18[\/latex].<\/p>\n

Fabric<\/strong> The drill team used [latex]14[\/latex] yards of fabric to make flags for one-third of the members. Find how much fabric, [latex]f[\/latex], they would need to make flags for the whole team by solving the equation [latex]\\Large\\frac{1}{3}\\normalsize f=14[\/latex].<\/p>\n

42 yards<\/p>\n<\/div>\n

 <\/p>\n

\n

writing exercises<\/h3>\n

Frida started to solve the equation [latex]-3x=36[\/latex] by adding [latex]3[\/latex] to both sides. Explain why Frida\u2019s method will result in the correct solution.<\/p>\n

Emiliano thinks [latex]x=40[\/latex] is the solution to the equation [latex]\\Large\\frac{1}{2}\\normalsize x=80[\/latex]. Explain why he is wrong.<\/p>\n

Answer will vary.<\/p>\n

<\/h2>\n<\/div>\n

<\/h2>\n

Solve Equations with Variables and Constants on Both Sides<\/h2>\n

Solve an Equation with Constants on Both Sides<\/strong><\/h3>\n

In the following exercises, solve the equation for the variable.<\/p>\n

[latex]6x - 2=40[\/latex]<\/p>\n

[latex]7x - 8=34[\/latex]<\/p>\n

6<\/p>\n

[latex]11w+6=93[\/latex]<\/p>\n

[latex]14y+7=91[\/latex]<\/p>\n

6<\/p>\n

[latex]3a+8=-46[\/latex]<\/p>\n

[latex]4m+9=-23[\/latex]<\/p>\n

\u22128<\/p>\n

[latex]-50=7n - 1[\/latex]<\/p>\n

[latex]-47=6b+1[\/latex]<\/p>\n

\u22128<\/p>\n

[latex]25=-9y+7[\/latex]<\/p>\n

[latex]29=-8x - 3[\/latex]<\/p>\n

\u22124<\/p>\n

[latex]-12p - 3=15[\/latex]<\/p>\n

[latex]-14\\text{q}-15=13[\/latex]<\/p>\n

\u22122<\/p>\n

Solve an Equation with Variables on Both Sides<\/strong>
\nIn the following exercises, solve the equation for the variable.<\/p>\n

[latex]8z=7z - 7[\/latex]<\/p>\n

[latex]9k=8k - 11[\/latex]<\/p>\n

\u221211<\/p>\n

[latex]4x+36=10x[\/latex]<\/p>\n

[latex]6x+27=9x[\/latex]<\/p>\n

9<\/p>\n

[latex]c=-3c - 20[\/latex]<\/p>\n

[latex]b=-4b - 15[\/latex]<\/p>\n

\u22123<\/p>\n

[latex]5q=44 - 6q[\/latex]<\/p>\n

[latex]7z=39 - 6z[\/latex]<\/p>\n

3<\/p>\n

[latex]3y+\\Large\\frac{1}{2}\\normalsize =2y[\/latex]<\/p>\n

[latex]8x+\\Large\\frac{3}{4}\\normalsize =7x[\/latex]<\/p>\n

\u22123\/4<\/p>\n

[latex]-12a - 8=-16a[\/latex]<\/p>\n

[latex]-15r - 8=-11r[\/latex]<\/p>\n

2<\/p>\n

Solve an Equation with Variables and Constants on Both Sides<\/strong>
\nIn the following exercises, solve the equations for the variable.<\/p>\n

[latex]6x - 15=5x+3[\/latex]<\/p>\n

[latex]4x - 17=3x+2[\/latex]<\/p>\n

19<\/p>\n

[latex]26+8d=9d+11[\/latex]<\/p>\n

[latex]21+6f=7f+14[\/latex]<\/p>\n

7<\/p>\n

[latex]3p - 1=5p - 33[\/latex]<\/p>\n

[latex]8q - 5=5q - 20[\/latex]<\/p>\n

\u22125<\/p>\n

[latex]4a+5=-a - 40[\/latex]<\/p>\n

[latex]9c+7=-2c - 37[\/latex]<\/p>\n

\u22124<\/p>\n

[latex]8y - 30=-2y+30[\/latex]<\/p>\n

[latex]12x - 17=-3x+13[\/latex]<\/p>\n

2<\/p>\n

[latex]2\\text{z}-4=23-\\text{z}[\/latex]<\/p>\n

[latex]3y - 4=12-y[\/latex]<\/p>\n

4<\/p>\n

[latex]\\Large\\frac{5}{4}\\normalsize c - 3=\\Large\\frac{1}{4}\\normalsize c - 16[\/latex]<\/p>\n

[latex]\\Large\\frac{4}{3}\\normalsize m - 7=\\Large\\frac{1}{3}\\normalsize m - 13[\/latex]<\/p>\n

6<\/p>\n

[latex]8-\\Large\\frac{2}{5}\\normalsize q=\\Large\\frac{3}{5}\\normalsize q+6[\/latex]<\/p>\n

[latex]11-\\Large\\frac{1}{4}\\normalsize a=\\Large\\frac{3}{4}\\normalsize a+4[\/latex]<\/p>\n

7<\/p>\n

[latex]\\Large\\frac{4}{3}\\normalsize n+9=\\Large\\frac{1}{3}\\normalsize n - 9[\/latex]<\/p>\n

[latex]\\Large\\frac{5}{4}\\normalsize a+15=\\Large\\frac{3}{4}\\normalsize a - 5[\/latex]<\/p>\n

\u221240<\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize y+7=\\Large\\frac{3}{4}\\normalsize y - 3[\/latex]<\/p>\n

[latex]\\Large\\frac{3}{5}\\normalsize p+2=\\Large\\frac{4}{5}\\normalsize p - 1[\/latex]<\/p>\n

3<\/p>\n

[latex]14n+8.25=9n+19.60[\/latex]<\/p>\n

[latex]13z+6.45=8z+23.75[\/latex]<\/p>\n

3.46<\/p>\n

[latex]2.4w - 100=0.8w+28[\/latex]<\/p>\n

[latex]2.7w - 80=1.2w+10[\/latex]<\/p>\n

60<\/p>\n

[latex]5.6r+13.1=3.5r+57.2[\/latex]<\/p>\n

[latex]6.6x - 18.9=3.4x+54.7[\/latex]<\/p>\n

23<\/p>\n

Solve an Equation Using the General Strategy<\/strong>
\nIn the following exercises, solve the linear equation using the general strategy.<\/p>\n

[latex]5\\left(x+3\\right)=75[\/latex]<\/p>\n

[latex]4\\left(y+7\\right)=64[\/latex]<\/p>\n

9<\/p>\n

[latex]8=4\\left(x - 3\\right)[\/latex]<\/p>\n

[latex]9=3\\left(x - 3\\right)[\/latex]<\/p>\n

6<\/p>\n

[latex]20\\left(y - 8\\right)=-60[\/latex]<\/p>\n

[latex]14\\left(y - 6\\right)=-42[\/latex]<\/p>\n

3<\/p>\n

[latex]-4\\left(2n+1\\right)=16[\/latex]<\/p>\n

[latex]-7\\left(3n+4\\right)=14[\/latex]<\/p>\n

\u22122<\/p>\n

[latex]3\\left(10+5r\\right)=0[\/latex]<\/p>\n

[latex]8\\left(3+3\\text{p}\\right)=0[\/latex]<\/p>\n

\u22121<\/p>\n

[latex]\\Large\\frac{2}{3}\\normalsize\\left(9c - 3\\right)=22[\/latex]<\/p>\n

[latex]\\Large\\frac{3}{5}\\normalsize\\left(10x - 5\\right)=27[\/latex]<\/p>\n

5<\/p>\n

[latex]5\\left(1.2u - 4.8\\right)=-12[\/latex]<\/p>\n

[latex]4\\left(2.5v - 0.6\\right)=7.6[\/latex]<\/p>\n

0.52<\/p>\n

[latex]0.2\\left(30n+50\\right)=28[\/latex]<\/p>\n

[latex]0.5\\left(16m+34\\right)=-15[\/latex]<\/p>\n

0.25<\/p>\n

[latex]-\\left(w - 6\\right)=24[\/latex]<\/p>\n

[latex]-\\left(t - 8\\right)=17[\/latex]<\/p>\n

\u22129<\/p>\n

[latex]9\\left(3a+5\\right)+9=54[\/latex]<\/p>\n

[latex]8\\left(6b - 7\\right)+23=63[\/latex]<\/p>\n

2<\/p>\n

[latex]10+3\\left(z+4\\right)=19[\/latex]<\/p>\n

[latex]13+2\\left(m - 4\\right)=17[\/latex]<\/p>\n

6<\/p>\n

[latex]7+5\\left(4-q\\right)=12[\/latex]<\/p>\n

[latex]-9+6\\left(5-k\\right)=12[\/latex]<\/p>\n

3\/2<\/p>\n

[latex]15-\\left(3r+8\\right)=28[\/latex]<\/p>\n

[latex]18-\\left(9r+7\\right)=-16[\/latex]<\/p>\n

3<\/p>\n

[latex]11 - 4\\left(y - 8\\right)=43[\/latex]<\/p>\n

[latex]18 - 2\\left(y - 3\\right)=32[\/latex]<\/p>\n

\u22124<\/p>\n

[latex]9\\left(p - 1\\right)=6\\left(2p - 1\\right)[\/latex]<\/p>\n

[latex]3\\left(4n - 1\\right)-2=8n+3[\/latex]<\/p>\n

2<\/p>\n

[latex]9\\left(2m - 3\\right)-8=4m+7[\/latex]<\/p>\n

[latex]5\\left(x - 4\\right)-4x=14[\/latex]<\/p>\n

34<\/p>\n

[latex]8\\left(x - 4\\right)-7x=14[\/latex]<\/p>\n

[latex]5+6\\left(3s - 5\\right)=-3+2\\left(8s - 1\\right)[\/latex]<\/p>\n

10<\/p>\n

[latex]-12+8\\left(x - 5\\right)=-4+3\\left(5x - 2\\right)[\/latex]<\/p>\n

[latex]4\\left(x - 1\\right)-8=6\\left(3x - 2\\right)-7[\/latex]<\/p>\n

2<\/p>\n

[latex]7\\left(2x - 5\\right)=8\\left(4x - 1\\right)-9[\/latex]<\/p>\n

\n

everyday math<\/h3>\n

Making a fence<\/strong><\/h4>\n

Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the width, [latex]w[\/latex], by solving the equation [latex]150=2\\left(w+15\\right)+2w[\/latex].<\/p>\n

30 feet<\/p>\n

Concert tickets<\/strong><\/h4>\n

At a school concert, the total value of tickets sold was [latex]{$1,506.}[\/latex] Student tickets sold for [latex]{$6}[\/latex] and adult tickets sold for [latex]{$9.}[\/latex] The number of adult tickets sold was [latex]5[\/latex] less than [latex]3[\/latex] times the number of student tickets. Find the number of student tickets sold, [latex]s[\/latex], by solving the equation [latex]6s+9\\left(3s - 5\\right)=1506[\/latex].<\/p>\n

Coins<\/strong> Rhonda has [latex]{$1.90}[\/latex] in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, [latex]n[\/latex], by solving the equation [latex]0.05n+0.10\\left(2n - 1\\right)=1.90[\/latex].<\/p>\n

8 nickels<\/p>\n

Fencing<\/strong><\/h4>\n

Micah has [latex]74[\/latex] feet of fencing to make a rectangular dog pen in his yard. He wants the length to be [latex]25[\/latex] feet more than the width. Find the length, [latex]L[\/latex], by solving the equation [latex]2L+2\\left(L - 25\\right)=74[\/latex].<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

\n

writing exercises<\/h3>\n

When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?<\/p>\n

Answers will vary.<\/p>\n

Solve the equation [latex]10x+14=-2x+38[\/latex], explaining all the steps of your solution.<\/p>\n

What is the first step you take when solving the equation [latex]3 - 7\\left(y - 4\\right)=38?[\/latex] Explain why this is your first step.<\/p>\n

Answers will vary.<\/p>\n

Solve the equation [latex]\\Large\\frac{1}{4}\\normalsize\\left(8x+20\\right)=3x - 4[\/latex] explaining all the steps of your solution as in the examples in this section.<\/p>\n

Using your own words, list the steps in the General Strategy for Solving Linear Equations.<\/p>\n

Answers will vary.<\/p>\n

Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

Solve Equations with Fraction or Decimal Coefficients<\/h2>\n

Solve equations with fraction coefficients<\/strong><\/h3>\n

In the following exercises, solve the equation by clearing the fractions.<\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]<\/p>\n

x<\/em> = \u22121<\/p>\n

[latex]\\Large\\frac{3}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{1}{4}[\/latex]<\/p>\n

[latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{2}{3}\\normalsize =-\\Large\\frac{3}{2}[\/latex]<\/p>\n

y<\/em> = \u22121<\/p>\n

[latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{1}{3}\\normalsize =-\\Large\\frac{7}{6}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{3}{4}[\/latex]<\/p>\n

[latex]a=\\Large\\frac{3}{4}[\/latex]<\/p>\n

[latex]\\Large\\frac{5}{8}\\normalsize b+\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]<\/p>\n

[latex]2=\\Large\\frac{1}{3}\\normalsize x-\\Large\\frac{1}{2}\\normalsize x+\\Large\\frac{2}{3}\\normalsize x[\/latex]<\/p>\n

x<\/em> = 4<\/p>\n

[latex]2=\\Large\\frac{3}{5}\\normalsize x-\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{2}{5}\\normalsize x[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize m-\\Large\\frac{4}{5}\\normalsize m+\\Large\\frac{1}{2}\\normalsize m=-1[\/latex]<\/p>\n

m<\/em> = 20<\/p>\n

[latex]\\Large\\frac{5}{6}\\normalsize n-\\Large\\frac{1}{4}\\normalsize n-\\Large\\frac{1}{2}\\normalsize n=-2[\/latex]<\/p>\n

[latex]x+\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{2}{3}\\normalsize x-\\Large\\frac{1}{2}[\/latex]<\/p>\n

x<\/em> = \u22123<\/p>\n

[latex]x+\\Large\\frac{3}{4}\\normalsize =\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{5}{4}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize w+\\Large\\frac{5}{4}\\normalsize =w-\\Large\\frac{1}{4}[\/latex]<\/p>\n

[latex]w=\\Large\\frac{9}{4}[\/latex]<\/p>\n

[latex]\\Large\\frac{3}{2}\\normalsize z+\\Large\\frac{1}{3}\\normalsize =z-\\Large\\frac{2}{3}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{12}\\normalsize x+\\Large\\frac{1}{6}[\/latex]<\/p>\n

x<\/em> = 1<\/p>\n

[latex]\\Large\\frac{1}{2}\\normalsize a-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{6}\\normalsize a+\\Large\\frac{1}{12}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize b+\\Large\\frac{1}{5}\\normalsize =\\Large\\frac{2}{5}\\normalsize b-\\Large\\frac{3}{5}[\/latex]<\/p>\n

b<\/em> = 12<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{2}{5}\\normalsize =\\Large\\frac{1}{5}\\normalsize x-\\Large\\frac{2}{5}[\/latex]<\/p>\n

[latex]1=\\Large\\frac{1}{6}\\normalsize\\left(12x - 6\\right)[\/latex]<\/p>\n

x<\/em> = 1<\/p>\n

[latex]1=\\Large\\frac{1}{5}\\normalsize\\left(15x - 10\\right)[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize\\left(p - 7\\right)=\\Large\\frac{1}{3}\\normalsize\\left(p+5\\right)[\/latex]<\/p>\n

p<\/em> = \u221241<\/p>\n

[latex]\\Large\\frac{1}{5}\\normalsize\\left(q+3\\right)=\\Large\\frac{1}{2}\\normalsize\\left(q - 3\\right)[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{2}\\normalsize\\left(x+4\\right)=\\Large\\frac{3}{4}[\/latex]<\/p>\n

[latex]x=-\\Large\\frac{5}{2}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize\\left(x+5\\right)=\\Large\\frac{5}{6}[\/latex]<\/p>\n

Solve Equations with Decimal Coefficients<\/strong><\/h3>\n

In the following exercises, solve the equation by clearing the decimals.<\/p>\n

[latex]0.6y+3=9[\/latex]<\/p>\n

y<\/em> = 10<\/p>\n

[latex]0.4y - 4=2[\/latex]<\/p>\n

[latex]3.6j - 2=5.2[\/latex]<\/p>\n

j<\/em> = 2<\/p>\n

[latex]2.1k+3=7.2[\/latex]<\/p>\n

[latex]0.4x+0.6=0.5x - 1.2[\/latex]<\/p>\n

x<\/em> = 18<\/p>\n

[latex]0.7x+0.4=0.6x+2.4[\/latex]<\/p>\n

[latex]0.23x+1.47=0.37x - 1.05[\/latex]<\/p>\n

x<\/em> = 18<\/p>\n

[latex]0.48x+1.56=0.58x - 0.64[\/latex]<\/p>\n

[latex]0.9x - 1.25=0.75x+1.75[\/latex]<\/p>\n

x<\/em> = 20<\/p>\n

[latex]1.2x - 0.91=0.8x+2.29[\/latex]<\/p>\n

[latex]0.05n+0.10\\left(n+8\\right)=2.15[\/latex]<\/p>\n

n<\/em> = 9<\/p>\n

[latex]0.05n+0.10\\left(n+7\\right)=3.55[\/latex]<\/p>\n

[latex]0.10d+0.25\\left(d+5\\right)=4.05[\/latex]<\/p>\n

d<\/em> = 8<\/p>\n

[latex]0.10d+0.25\\left(d+7\\right)=5.25[\/latex]<\/p>\n

[latex]0.05\\left(q - 5\\right)+0.25q=3.05[\/latex]<\/p>\n

q<\/em> = 11<\/p>\n

[latex]0.05\\left(q - 8\\right)+0.25q=4.10[\/latex]<\/p>\n

\n

Everyday math<\/h3>\n

Coins<\/strong> Taylor has [latex]{$2.00}[\/latex] in dimes and pennies. The number of pennies is [latex]2[\/latex] more than the number of dimes. Solve the equation [latex]0.10d+0.01\\left(d+2\\right)=2[\/latex] for [latex]d[\/latex], the number of dimes.<\/p>\n

d<\/em> = 18<\/p>\n

Stamps<\/strong> Travis bought [latex]{$9.45}[\/latex] worth of [latex]\\text{49-cent}[\/latex] stamps and [latex]\\text{21-cent}[\/latex] stamps. The number of [latex]\\text{21-cent}[\/latex] stamps was [latex]5[\/latex] less than the number of [latex]\\text{49-cent}[\/latex] stamps. Solve the equation [latex]0.49s+0.21\\left(s - 5\\right)=9.45[\/latex] for [latex]s[\/latex], to find the number of [latex]\\text{49-cent}[\/latex] stamps Travis bought.<\/p>\n<\/div>\n

 <\/p>\n

\n

writing exercises<\/h3>\n

Explain how to find the least common denominator of [latex]\\Large\\frac{3}{8}\\normalsize ,\\Large\\frac{1}{6}\\normalsize ,\\text{and}\\Large\\frac{2}{3}[\/latex].<\/p>\n

Answers will vary.<\/p>\n

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?<\/p>\n

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?<\/p>\n

Answers will vary.<\/p>\n

In the equation [latex]0.35x+2.1=3.85[\/latex], what is the LCD? How do you know?<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

Chapter Review Exercises<\/h3>\n
\n

Solve Equations using the Subtraction and Addition Properties of Equality<\/h3>\n

In the following exercises, determine whether the given number is a solution to the equation.<\/p>\n

[latex]x+16=31,x=15[\/latex]<\/p>\n

yes<\/p>\n

[latex]w - 8=5,w=3[\/latex]<\/p>\n

[latex]-9n=45,n=54[\/latex]<\/p>\n

no<\/p>\n

[latex]4a=72,a=18[\/latex]<\/p>\n

In the following exercises, solve the equation using the Subtraction Property of Equality.<\/p>\n

[latex]x+7=19[\/latex]<\/p>\n

12<\/p>\n

[latex]y+2=-6[\/latex]<\/p>\n

[latex]a+\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{5}{3}[\/latex]<\/p>\n

[latex]a=\\Large\\frac{4}{3}[\/latex]<\/p>\n

[latex]n+3.6=5.1[\/latex]<\/p>\n

In the following exercises, solve the equation using the Addition Property of Equality.<\/p>\n

[latex]u - 7=10[\/latex]<\/p>\n

u<\/em> = 17<\/p>\n

[latex]x - 9=-4[\/latex]<\/p>\n

[latex]c-\\Large\\frac{3}{11}\\normalsize =\\Large\\frac{9}{11}[\/latex]<\/p>\n

[latex]c=\\Large\\frac{12}{11}[\/latex]<\/p>\n

[latex]p - 4.8=14[\/latex]<\/p>\n

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

[latex]n - 12=32[\/latex]<\/p>\n

n<\/em> = 44<\/p>\n

[latex]y+16=-9[\/latex]<\/p>\n

[latex]f+\\Large\\frac{2}{3}\\normalsize =4[\/latex]<\/p>\n

[latex]f=\\Large\\frac{10}{3}[\/latex]<\/p>\n

[latex]d - 3.9=8.2[\/latex]<\/p>\n

[latex]y+8 - 15=-3[\/latex]<\/p>\n

y<\/em> = 4<\/p>\n

[latex]7x+10 - 6x+3=5[\/latex]<\/p>\n

[latex]6\\left(n - 1\\right)-5n=-14[\/latex]<\/p>\n

n<\/em> = \u22128<\/p>\n

[latex]8\\left(3p+5\\right)-23\\left(p - 1\\right)=35[\/latex]<\/p>\n

In the following exercises, translate each English sentence into an algebraic equation and then solve it.<\/p>\n

The sum of [latex]-6[\/latex] and [latex]m[\/latex] is [latex]25[\/latex].<\/p>\n

\u22126 + m<\/em> = 25; m<\/em> = 31<\/p>\n

Four less than [latex]n[\/latex] is [latex]13[\/latex].<\/p>\n

In the following exercises, translate into an algebraic equation and solve.<\/p>\n

Rochelle\u2019s daughter is [latex]11[\/latex] years old. Her son is [latex]3[\/latex] years younger. How old is her son?<\/p>\n

s<\/em> = 11 \u2212 3; 8 years old<\/p>\n

Tan weighs [latex]146[\/latex] pounds. Minh weighs [latex]15[\/latex] pounds more than Tan. How much does Minh weigh?<\/p>\n

Peter paid [latex]{$9.75}[\/latex] to go to the movies, which was [latex]{$46.25}[\/latex] less than he paid to go to a concert. How much did he pay for the concert?<\/p>\n

c<\/em> \u2212 46.25 = 9.75; $56.00<\/p>\n

Elissa earned [latex]{$152.84}[\/latex] this week, which was [latex]{$21.65}[\/latex] more than she earned last week. How much did she earn last week?<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

\n

Solve Equations using the Division and Multiplication Properties of Equality<\/h3>\n

In the following exercises, solve each equation using the Division Property of Equality.<\/p>\n

[latex]8x=72[\/latex]<\/p>\n

x<\/em> = 9<\/p>\n

[latex]13a=-65[\/latex]<\/p>\n

[latex]0.25p=5.25[\/latex]<\/p>\n

p<\/em> = 21<\/p>\n

[latex]-y=4[\/latex]<\/p>\n

In the following exercises, solve each equation using the Multiplication Property of Equality.<\/p>\n

[latex]\\Large\\frac{n}{6}\\normalsize =18[\/latex]<\/p>\n

n<\/em> = 108<\/p>\n

[latex]\\Large\\frac{y}{-10}\\normalsize =30[\/latex]<\/p>\n

[latex]36=\\Large\\frac{3}{4}\\normalsize x[\/latex]<\/p>\n

x<\/em> = 48<\/p>\n

[latex]\\Large\\frac{5}{8}\\normalsize u=\\Large\\frac{15}{16}[\/latex]<\/p>\n

In the following exercises, solve each equation.<\/p>\n

[latex]-18m=-72[\/latex]<\/p>\n

m<\/em> = 4<\/p>\n

[latex]\\Large\\frac{c}{9}\\normalsize =36[\/latex]<\/p>\n

[latex]0.45x=6.75[\/latex]<\/p>\n

x<\/em> = 15<\/p>\n

[latex]\\Large\\frac{11}{12}\\normalsize =\\Large\\frac{2}{3}\\normalsize y[\/latex]<\/p>\n

[latex]5r - 3r+9r=35 - 2[\/latex]<\/p>\n

r<\/em> = 3<\/p>\n

[latex]24x+8x - 11x=-7 - 14[\/latex]<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

\n

Solve Equations with Variables and Constants on Both Sides<\/h3>\n

In the following exercises, solve the equations with constants on both sides.<\/p>\n

[latex]8p+7=47[\/latex]<\/p>\n

p<\/em> = 5<\/p>\n

[latex]10w - 5=65[\/latex]<\/p>\n

[latex]3x+19=-47[\/latex]<\/p>\n

x<\/em> = \u221222<\/p>\n

[latex]32=-4 - 9n[\/latex]<\/p>\n

In the following exercises, solve the equations with variables on both sides.<\/p>\n

[latex]7y=6y - 13[\/latex]<\/p>\n

y<\/em> = \u221213<\/p>\n

[latex]5a+21=2a[\/latex]<\/p>\n

[latex]k=-6k - 35[\/latex]<\/p>\n

k<\/em> = \u22125<\/p>\n

[latex]4x-\\Large\\frac{3}{8}\\normalsize =3x[\/latex]<\/p>\n

In the following exercises, solve the equations with constants and variables on both sides.<\/p>\n

[latex]12x - 9=3x+45[\/latex]<\/p>\n

x<\/em> = 6<\/p>\n

[latex]5n - 20=-7n - 80[\/latex]<\/p>\n

[latex]4u+16=-19-u[\/latex]<\/p>\n

u<\/em> = \u22127<\/p>\n

[latex]\\Large\\frac{5}{8}\\normalsize c - 4=\\Large\\frac{3}{8}\\normalsize c+4[\/latex]<\/p>\n

In the following exercises, solve each linear equation using the general strategy.<\/p>\n

[latex]6\\left(x+6\\right)=24[\/latex]<\/p>\n

x<\/em> = \u22122<\/p>\n

[latex]9\\left(2p - 5\\right)=72[\/latex]<\/p>\n

[latex]-\\left(s+4\\right)=18[\/latex]<\/p>\n

s<\/em> = \u221222<\/p>\n

[latex]8+3\\left(n - 9\\right)=17[\/latex]<\/p>\n

[latex]23 - 3\\left(y - 7\\right)=8[\/latex]<\/p>\n

y<\/em> = 12<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize\\left(6m+21\\right)=m - 7[\/latex]<\/p>\n

[latex]8\\left(r - 2\\right)=6\\left(r+10\\right)[\/latex]<\/p>\n

r<\/em> = 38<\/p>\n

[latex]5+7\\left(2 - 5x\\right)=2\\left(9x+1\\right)-\\left(13x - 57\\right)[\/latex]<\/p>\n

[latex]4\\left(3.5y+0.25\\right)=365[\/latex]<\/p>\n

y<\/em> = 26<\/p>\n

[latex]0.25\\left(q - 8\\right)=0.1\\left(q+7\\right)[\/latex]<\/p>\n

<\/h2>\n<\/div>\n

 <\/p>\n

\n

Solve Equations with Fraction or Decimal Coefficients<\/h3>\n

In the following exercises, solve each equation by clearing the fractions.<\/p>\n

[latex]\\Large\\frac{2}{5}\\normalsize n-\\Large\\frac{1}{10}\\normalsize =\\Large\\frac{7}{10}[\/latex]<\/p>\n

n<\/em> = 2<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize x+\\Large\\frac{1}{5}\\normalsize x=8[\/latex]<\/p>\n

[latex]\\Large\\frac{3}{4}\\normalsize a-\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{5}{6}[\/latex]<\/p>\n

[latex]a=\\Large\\frac{14}{3}[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{2}\\normalsize\\left(k+3\\right)=\\Large\\frac{1}{3}\\normalsize\\left(k+16\\right)[\/latex]<\/p>\n

In the following exercises, solve each equation by clearing the decimals.<\/p>\n

[latex]0.8x - 0.3=0.7x+0.2[\/latex]<\/p>\n

x<\/em> = 5<\/p>\n

[latex]0.36u+2.55=0.41u+6.8[\/latex]<\/p>\n

[latex]0.6p - 1.9=0.78p+1.7[\/latex]<\/p>\n

p<\/em> = \u221220<\/p>\n

[latex]0.10d+0.05\\left(d - 4\\right)=2.05[\/latex]<\/p>\n

<\/h1>\n<\/div>\n

 <\/p>\n

\n

Chapter Practice Test<\/h3>\n

Determine whether each number is a solution to the equation.<\/p>\n

[latex]3x+5=23[\/latex].<\/p>\n

\u24d0 [latex]6[\/latex]
\n\u24d1 [latex]\\Large\\frac{23}{5}[\/latex]<\/p>\n

\u24d0 yes
\n\u24d1 no<\/p>\n

In the following exercises, solve each equation.<\/p>\n

[latex]n - 18=31[\/latex]<\/p>\n

[latex]9c=144[\/latex]<\/p>\n

c<\/em> = 16<\/p>\n

[latex]4y - 8=16[\/latex]<\/p>\n

[latex]-8x - 15+9x - 1=-21[\/latex]<\/p>\n

x<\/em> = \u22125<\/p>\n

[latex]-15a=120[\/latex]<\/p>\n

[latex]\\Large\\frac{2}{3}\\normalsize x=6[\/latex]<\/p>\n

x<\/em> = 9<\/p>\n

[latex]x+3.8=8.2[\/latex]<\/p>\n

[latex]10y=-5y+60[\/latex]<\/p>\n

y<\/em> = 4<\/p>\n

[latex]8n+2=6n+12[\/latex]<\/p>\n

[latex]9m - 2 - 4m+m=42 - 8[\/latex]<\/p>\n

m<\/em> = 6<\/p>\n

[latex]-5\\left(2x+1\\right)=45[\/latex]<\/p>\n

[latex]-\\left(d+9\\right)=23[\/latex]<\/p>\n

d<\/em> = \u221232<\/p>\n

[latex]\\Large\\frac{1}{3}\\normalsize\\left(6m+21\\right)=m - 7[\/latex]<\/p>\n

[latex]2\\left(6x+5\\right)-8=-22[\/latex]<\/p>\n

x<\/em> = \u22122<\/p>\n

[latex]8\\left(3a+5\\right)-7\\left(4a - 3\\right)=20 - 3a[\/latex]<\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize p+\\Large\\frac{1}{3}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/p>\n

[latex]p=\\Large\\frac{2}{3}[\/latex]<\/p>\n

[latex]0.1d+0.25\\left(d+8\\right)=4.1[\/latex]<\/p>\n

Translate and solve: The difference of twice [latex]x[\/latex] and [latex]4[\/latex] is [latex]16[\/latex].<\/p>\n

2x<\/em> \u2212 4 = 16; x<\/em> = 10<\/p>\n

Samuel paid [latex]{$25.82}[\/latex] for gas this week, which was [latex]{$3.47}[\/latex] less than he paid last week. How much did he pay last week?<\/p>\n

Determine Whether a Decimal is a Solution of an Equation<\/b>
\nIn the following exercises, determine whether each number is a solution of the given equation.<\/span><\/p>\n

[latex]x - 0.8=2.3[\/latex]<\/span><\/p>\n

\u24d0<\/span> [latex]x=2[\/latex] <\/span>\u24d1<\/span> [latex]x=-1.5[\/latex] <\/span>\u24d2<\/span> [latex]x=3.1[\/latex]<\/span><\/p>\n

\u24d0<\/span> no
\n<\/span>\u24d1<\/span> no
\n<\/span>\u24d2<\/span> yes<\/span><\/p>\n

[latex]y+0.6=-3.4[\/latex]<\/span><\/p>\n

\u24d0<\/span> [latex]y=-4[\/latex] <\/span>\u24d1<\/span> [latex]y=-2.8[\/latex] <\/span>\u24d2<\/span> [latex]y=2.6[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{h}{1.5}\\normalsize =-4.3[\/latex]<\/span><\/p>\n

\u24d0<\/span> [latex]h=6.45[\/latex] <\/span>\u24d1<\/span> [latex]h=-6.45[\/latex] <\/span>\u24d2<\/span> [latex]h=-2.1[\/latex]<\/span><\/p>\n

\u24d0<\/span> no
\n<\/span>\u24d1<\/span> yes
\n<\/span>\u24d2<\/span> no<\/span><\/p>\n

[latex]0.75k=-3.6[\/latex]<\/span><\/p>\n

\u24d0<\/span> [latex]k=-0.48[\/latex] <\/span>\u24d1<\/span> [latex]k=-4.8[\/latex] <\/span>\u24d2<\/span> [latex]k=-2.7[\/latex]<\/span><\/p>\n

Solve Equations with Decimals<\/b>
\n<\/span><\/h4>\n

In the following exercises, solve the equation.<\/span><\/p>\n

[latex]y+2.9=5.7[\/latex]<\/span><\/p>\n

y<\/i> = 2.8<\/span><\/p>\n

[latex]m+4.6=6.5[\/latex]<\/span><\/p>\n

[latex]f+3.45=2.6[\/latex]<\/span><\/p>\n

f<\/i> = \u22120.85<\/span><\/p>\n

[latex]h+4.37=3.5[\/latex]<\/span><\/p>\n

[latex]a+6.2=-1.7[\/latex]<\/span><\/p>\n

a<\/i> = \u22127.9<\/span><\/p>\n

[latex]b+5.8=-2.3[\/latex]<\/span><\/p>\n

[latex]c+1.15=-3.5[\/latex]<\/span><\/p>\n

c<\/i> = \u22124.65<\/span><\/p>\n

[latex]d+2.35=-4.8[\/latex]<\/span><\/p>\n

[latex]n - 2.6=1.8[\/latex]<\/span><\/p>\n

n<\/i> = 4.4<\/span><\/p>\n

[latex]p - 3.6=1.7[\/latex]<\/span><\/p>\n

[latex]x - 0.4=-3.9[\/latex]<\/span><\/p>\n

x<\/i> = \u22123.5<\/span><\/p>\n

[latex]y - 0.6=-4.5[\/latex]<\/span><\/p>\n

[latex]j - 1.82=-6.5[\/latex]<\/span><\/p>\n

j<\/i> = \u22124.68<\/span><\/p>\n

[latex]k - 3.19=-4.6[\/latex]<\/span><\/p>\n

[latex]m - 0.25=-1.67[\/latex]<\/span><\/p>\n

m<\/i> = \u22121.42<\/span><\/p>\n

[latex]q - 0.47=-1.53[\/latex]<\/span><\/p>\n

[latex]0.5x=3.5[\/latex]<\/span><\/p>\n

x<\/i> = 7<\/span><\/p>\n

[latex]0.4p=9.2[\/latex]<\/span><\/p>\n

[latex]-1.7c=8.5[\/latex]<\/span><\/p>\n

c<\/i> = \u22125<\/span><\/p>\n

[latex]-2.9x=5.8[\/latex]<\/span><\/p>\n

[latex]-1.4p=-4.2[\/latex]<\/span><\/p>\n

p<\/i> = 3<\/span><\/p>\n

[latex]-2.8m=-8.4[\/latex]<\/span><\/p>\n

[latex]-120=1.5q[\/latex]<\/span><\/p>\n

q<\/i> = \u221280<\/span><\/p>\n

[latex]-75=1.5y[\/latex]<\/span><\/p>\n

[latex]0.24x=4.8[\/latex]<\/span><\/p>\n

x<\/i> = 20<\/span><\/p>\n

[latex]0.18n=5.4[\/latex]<\/span><\/p>\n

[latex]-3.4z=-9.18[\/latex]<\/span><\/p>\n

z<\/i> = 2.7<\/span><\/p>\n

[latex]-2.7u=-9.72[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{a}{0.4}\\normalsize =-20[\/latex]<\/span><\/p>\n

a<\/i> = \u22128<\/span><\/p>\n

[latex]\\Large\\frac{b}{0.3}\\normalsize =-9[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{x}{0.7}\\normalsize =-0.4[\/latex]<\/span><\/p>\n

x<\/i> = \u22120.28<\/span><\/p>\n

[latex]\\Large\\frac{y}{0.8}\\normalsize =-0.7[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{p}{-5}\\normalsize =-1.65[\/latex]<\/span><\/p>\n

p<\/i> = 8.25<\/span><\/p>\n

[latex]\\Large\\frac{q}{-4}\\normalsize =-5.92[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{r}{-1.2}\\normalsize =-6[\/latex]<\/span><\/p>\n

r<\/i> = 7.2<\/span><\/p>\n

[latex]\\Large\\frac{s}{-1.5}\\normalsize =-3[\/latex]<\/span><\/p>\n

Mixed Practice<\/b>
\n<\/span><\/h4>\n

In the following exercises, solve the equation. Then check your solution.<\/span><\/p>\n

[latex]x - 5=-11[\/latex]<\/span><\/p>\n

x<\/i> = \u22126<\/span><\/p>\n

[latex]-\\Large\\frac{2}{5}\\normalsize =x+\\Large\\frac{3}{4}[\/latex]<\/span><\/p>\n

[latex]p+8=-2[\/latex]<\/span><\/p>\n

p<\/i> = \u221210<\/span><\/p>\n

[latex]p+\\Large\\frac{2}{3}\\normalsize =\\Large\\frac{1}{12}[\/latex]<\/span><\/p>\n

[latex]-4.2m=-33.6[\/latex]<\/span><\/p>\n

m<\/i> = 8<\/span><\/p>\n

[latex]q+9.5=-14[\/latex]<\/span><\/p>\n

[latex]q+\\Large\\frac{5}{6}\\normalsize =\\Large\\frac{1}{12}[\/latex]<\/span><\/p>\n

[latex]q=-\\Large\\frac{3}{4}[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{8.6}{15}\\normalsize =-d[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{7}{8}\\normalsize m=\\Large\\frac{1}{10}[\/latex]<\/span><\/p>\n

[latex]m=\\Large\\frac{4}{35}[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{j}{-6.2}\\normalsize =-3[\/latex]<\/span><\/p>\n

[latex]-\\Large\\frac{2}{3}\\normalsize =y+\\Large\\frac{3}{8}[\/latex]<\/span><\/p>\n

[latex]y=-\\Large\\frac{25}{24}[\/latex]<\/span><\/p>\n

[latex]s - 1.75=-3.2[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{11}{20}\\normalsize =-f[\/latex]<\/span><\/p>\n

[latex]f=-\\Large\\frac{11}{20}[\/latex]<\/span><\/p>\n

[latex]-3.6b=2.52[\/latex]<\/span><\/p>\n

[latex]-4.2a=3.36[\/latex]<\/span><\/p>\n

a<\/i> = \u22120.8<\/span><\/p>\n

[latex]-9.1n=-63.7[\/latex]<\/span><\/p>\n

[latex]r - 1.25=-2.7[\/latex]<\/span><\/p>\n

r<\/i> = \u22121.45<\/span><\/p>\n

[latex]\\Large\\frac{1}{4}\\normalsize n=\\Large\\frac{7}{10}[\/latex]<\/span><\/p>\n

[latex]\\Large\\frac{h}{-3}\\normalsize =-8[\/latex]<\/span><\/p>\n

h<\/i> = 24<\/span><\/p>\n

[latex]y - 7.82=-16[\/latex]<\/span><\/p>\n

Translate to an Equation and Solve<\/b>
\n<\/span><\/h4>\n

In the following exercises, translate and solve.<\/span><\/p>\n

The difference of [latex]n[\/latex] and [latex]1.9[\/latex] is [latex]3.4[\/latex].<\/span><\/p>\n

[latex]n - 1.9=3.4;5.3[\/latex]<\/span><\/p>\n

The difference [latex]n[\/latex] and [latex]1.5[\/latex] is [latex]0.8[\/latex].<\/span><\/p>\n

The product of [latex]-6.2[\/latex] and [latex]x[\/latex] is [latex]-4.96[\/latex].<\/span><\/p>\n

\u22126.2x<\/i> = \u22124.96; 0.8<\/span><\/p>\n

The product of [latex]-4.6[\/latex] and [latex]x[\/latex] is [latex]-3.22[\/latex].<\/span><\/p>\n

The quotient of [latex]y[\/latex] and [latex]-1.7[\/latex] is [latex]-5[\/latex].<\/span><\/p>\n

[latex]\\Large\\frac{y}{-1.7}\\normalsize =-5;8.5[\/latex]<\/span><\/p>\n

The quotient of [latex]z[\/latex] and [latex]-3.6[\/latex] is [latex]3[\/latex].<\/span><\/p>\n

The sum of [latex]n[\/latex] and [latex]-7.3[\/latex] is [latex]2.4[\/latex].<\/span><\/p>\n

n<\/i> + (\u22127.3) = 2.4; 9.7<\/span><\/p>\n

The sum of [latex]n[\/latex] and [latex]-5.1[\/latex] is [latex]3.8[\/latex].<\/span><\/p>\n

<\/h2>\n<\/div>\n

<\/h3>\n
\n

Everyday math<\/h3>\n

Shawn bought a pair of shoes on sale for [latex]$78[\/latex] . Solve the equation [latex]0.75p=78[\/latex] to find the original price of the shoes, [latex]p[\/latex].<\/span><\/p>\n

$104<\/span><\/p>\n

Mary bought a new refrigerator. The total price including sales tax was [latex]{$1,350}[\/latex]. Find the retail price, [latex]r[\/latex], of the refrigerator before tax by solving the equation [latex]1.08r=1,350[\/latex].<\/span><\/p>\n<\/div>\n

 <\/p>\n

\n

writing exercises<\/h3>\n

Think about solving the equation [latex]1.2y=60[\/latex], but do not actually solve it. Do you think the solution should be greater than [latex]60[\/latex] or less than [latex]60?[\/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.<\/span><\/p>\n

Answers will vary.<\/span><\/p>\n

Think about solving the equation [latex]0.8x=200[\/latex], but do not actually solve it. Do you think the solution should be greater than [latex]200[\/latex] or less than [latex]200?[\/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.<\/span><\/p>\n<\/div>\n

 <\/p>\n

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Specific attribution<\/div>