{"id":1042,"date":"2020-08-12T14:18:20","date_gmt":"2020-08-12T18:18:20","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-with-variables-and-constants-on-both-sides\/"},"modified":"2021-03-24T10:55:37","modified_gmt":"2021-03-24T14:55:37","slug":"solve-equations-with-variables-and-constants-on-both-sides","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-with-variables-and-constants-on-both-sides\/","title":{"raw":"5.3 Solve Equations with Variables and Constants on Both Sides","rendered":"5.3 Solve Equations with Variables and Constants on Both Sides"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Solve an equation with constants on both sides<\/li>\n \t<li>Solve an equation with variables on both sides<\/li>\n \t<li>Solve an equation with variables and constants on both sides<\/li>\n \t<li>Solve equations using a general strategy<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 id=\"fs-id1166497354586\" data-type=\"note\">Solve an Equation with Constants on Both Sides<\/h1>\n<div class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166491426623\">You may have noticed that in all the equations we have solved so far, all the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> terms were on only one side of the equation with the <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> on the other side. This does not happen all the time\u2014so now we\u2019ll see how to solve equations where the variable terms and\/or constant terms are on both sides of the equation.<\/p>\n<p id=\"fs-id1474518\">Our strategy will involve choosing one side of the equation to be the variable side, and the other side of the equation to be the constant side. Then, we will use the Subtraction and Addition Properties of Equality, step by step, to get all the variable terms together on one side of the equation and the constant terms together on the other side.<\/p>\n<p id=\"fs-id1166493722197\">By doing this, we will transform the equation that started with variables and constants on both sides into the form \\(ax=b\\). We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494591529\" data-type=\"problem\">\n<p id=\"fs-id1166494722150\">Solve: \\(4x+6=-14\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492789016\" data-type=\"solution\">\n<p id=\"fs-id1166484083743\">In this equation, the variable is only on the left side. It makes sense to call the left side the variable side. Therefore, the right side will be the constant side. We\u2019ll write the labels above the equation to help us remember what goes where.<\/p>\n\n<table id=\"eip-id1168467380704\" class=\"unnumbered unstyled\" summary=\"The top line says 4x plus 6 equals negative 14. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says, \u201cSince the left side is the variable side, the 6 is out of place. We must 'undo' adding 6 by subtracting 6, and to keep the equality we must subtract 6 from both sides. Use the Subtraction Property of Equality.\u201d Beside this is 4x plus 6 minus a red 6 equals negative 14 minus a red 6. The next line says \u201cSimplify\u201d and shows 4x equals negative 20. Below this, it says \u201cNow all the xs are on the left and the constant on the right.\u201d The next line says \u201cUse the Division Property of Equality\u201d and shows 4x over a red 4 equals negative 20 over a red 4. The next line says \u201cSimplify\u201d and shows x equals negative 5. The last step says \u201cCheck\u201d and shows 4x plus 6 equals negative 14. Below this is 4 times a red negative 5 plus 6, equal sign with a question mark, negative 14. Below is negative 20 plus 6, equal sign with a question mark, negative 14. The last line says negative 14 equals negative 14 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168467580178\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_03_039_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Since the left side is the variable side, the 6 is out of place. We must \"undo\" adding 6 by subtracting 6, and to keep the equality we must subtract 6 from both sides. Use the Subtraction Property of Equality.<\/td>\n<td><span id=\"eip-id1168468595447\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168469636495\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Now all the \\(x\\)s are on the left and the constant on the right.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Division Property of Equality.<\/td>\n<td><span id=\"eip-id1168468510734\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467161449\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168469706628\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Let \\(x=-5\\).<\/td>\n<td><span id=\"eip-id1168469888129\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469781731\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466173400\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492881928\" data-type=\"problem\">\n<p id=\"fs-id1731988\">Solve: \\(3x+4=-8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1457111\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166493265803\"><em data-effect=\"italics\">x<\/em> = \u22124<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497370080\" data-type=\"problem\">\n<p id=\"fs-id1912137\">Solve: \\(5a+3=-37\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166488289045\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166498100876\"><em data-effect=\"italics\">a<\/em> = \u22128<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166498437180\">Solve: \\(2y-7=15\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166491426141\" data-type=\"solution\">\n<p id=\"fs-id1895587\">Notice that the variable is only on the left side of the equation, so this will be the variable side and the right side will be the constant side. Since the left side is the variable side, the \\(7\\) is out of place. It is subtracted from the \\(2y\\), so to \u2018undo\u2019 subtraction, add \\(7\\) to both sides.<\/p>\n\n<table id=\"eip-id1168469592645\" style=\"width: 100%;\" summary=\"The first line says 2y minus 7 equals 15. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says \u201cAdd 7 to both sides\u201d and shows 2y minus 7 plus a red 7 equals 15 plus a red 7. The next line says \u201cSimplify\u201d and shows 2y equals 22. Below it says \u201cThe variables are now on one side and the constants on the other.\u201d The next line says \u201cDivide both sides by 2\u201d and shows 2y over a red 2 equals 22 over a red 2. The next line says \u201cSimplify\u201d and shows y equals 11. The next line says \u201cCheck\u201d and shows 2y minus 7 equals 15. Below is \u201cSubstitute y equals 11\u201d and shows 2 times a red 11 minus 7, equal sign with a question mark, 15. Below is 22 minus 7, equal sign with a question mark, 15. The last line says 15 equals 15, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468593491\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add 7 to both sides.<\/td>\n<td><span id=\"eip-id1168468264489\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467251501\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">The variables are now on one side and the constants on the other.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1168468309146\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168468455363\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468406041\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute: \\(y=11\\).<\/td>\n<td><span id=\"eip-id1168467196582\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468627978\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467473346\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492075765\" data-type=\"problem\">\n<p id=\"fs-id1166492068788\">Solve: \\(5y-9=16\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1431377\"><em data-effect=\"italics\">y<\/em> = 5<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1304456\" data-type=\"problem\">\n\nSolve: \\(3m-8=19\\).\n\n<\/div>\n<div id=\"fs-id1324771\" data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">m<\/em> = 9\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1515036\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve an Equation with Variables on Both Sides<\/h1>\n<p id=\"fs-id1390876\">What if there are variables on both sides of the equation? We will start like we did above\u2014choosing a <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> side and a constant side, and then use the Subtraction and Addition Properties of Equality to collect all variables on one side and all <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> on the other side. Remember, what you do to the left side of the equation, you must do to the right side too.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1302551\" data-type=\"problem\">\n<p id=\"fs-id1166491232107\">Solve: \\(5x=4x+7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1858532\" data-type=\"solution\">\n<div data-type=\"title\">Solution<\/div>\n<p id=\"fs-id1832872\">Here the variable, \\(x\\), is on both sides, but the constants appear only on the right side, so let\u2019s make the right side the \u201cconstant\u201d side. Then the left side will be the \u201cvariable\u201d side.<\/p>\n\n<table id=\"eip-id1168465095460\" style=\"width: 100%;\" summary=\"The first line says 5x equals 4x plus 7. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says \u201cWe don't want any variables on the right, so subtract the 4x from both sides.\u201d Beside that is 5x minus a red 4x equals 4x minus a red 4x plus 7. The next line says \u201cSimplify\u201d and shows x equals 7. Below is \u201cWe have all the variables on one side and the constants on the other. We have solved the equation.\u201d The next line says \u201cCheck\u201d and shows 5x equals 4x plus 7. Below is \u201cSubstitute 7 for x\u201d and 5 times a red 7 equals 4 times a red 7 plus 7. Below that is 35 equals 28 plus 7, then 35 equals 35.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468630242\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We don't want any variables on the right, so subtract the \\(4x\\).<\/td>\n<td><span id=\"eip-id1168468653139\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467114351\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We have all the variables on one side and the constants on the other. We have solved the equation.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468467076\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute 7 for \\(x\\).<\/td>\n<td><span id=\"eip-id1168468229247\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468264497\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468711064\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1470170\" data-type=\"problem\">\n<p id=\"fs-id1445738\">Solve: \\(6n=5n+10\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">n<\/em> = 10\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1436190\" data-type=\"problem\">\n<p id=\"fs-id1166493760719\">Solve: \\(-6c=-7c+1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166498435818\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1297432\"><em data-effect=\"italics\">c<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497309664\" data-type=\"problem\">\n<p id=\"fs-id1403520\">Solve: \\(5y-8=7y\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1355584\" data-type=\"solution\">\n\nThe only constant, \\(-8\\), is on the left side of the equation and variable, \\(y\\), is on both sides. Let\u2019s leave the constant on the left and collect the variables to the right.\n<table id=\"eip-id1168468768462\" style=\"width: 100%;\" summary=\"The first line says 5y minus 8 equals 7y. The left side is labeled \u201cconstant\u201d in red and the right side is labeled \u201cvariable\u201d in red. The next line says \u201cSubtract 5y from both sides\u201d and shows 5y minus a red 5y minus 8 equals 7y minus a red 5y. The next line says \u201cSimplify\u201d and shows negative 8 equals 2y. The next line says \u201cWe have the variables on the right and the constants on the left. Divide both sides by 2.\u201d Beside that is negative 8 over a red 2 equals 2y over a red 2. The next line says \u201cSimplify\u201d and shows negative 4 equals y. The next line says \u201cRewrite with the variable on the left\u201d and shows y equals negative 4. The last step says \u201cCheck. Let y equal negative 4.\u201d Beside that is 5y minus 8 equals 7y, then 5 times a red negative 4 minus 8 equals 7 times a red negative 4, then negative 20 minus 8 equals negative 28, then negative 28 equals negative 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468713810\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(5y\\) from both sides.<\/td>\n<td><span id=\"eip-id1168467116420\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467187881\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have the variables on the right and the constants on the left. Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1168467251083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467129401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the variable on the left.<\/td>\n<td><span id=\"eip-id1168468394421\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(y=-4\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468727587\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168467314260\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468411184\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468411200\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166483685326\" data-type=\"problem\">\n\nSolve: \\(3p-14=5p\\).\n\n<\/div>\n<div id=\"fs-id1691348\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1470064\"><em data-effect=\"italics\">p<\/em> = \u22127<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497310585\" data-type=\"problem\">\n<p id=\"fs-id1166494705142\">Solve: \\(8m+9=5m\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491402673\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1559521\"><em data-effect=\"italics\">m<\/em> = \u22123<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166482688772\" data-type=\"exercise\">\n<div id=\"fs-id1166483685326\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166489093428\" data-type=\"problem\">\n<p id=\"fs-id1558937\">Solve: \\(7x=-x+24\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492723804\" data-type=\"solution\">\n<p id=\"fs-id1166498045277\">The only constant, \\(24\\), is on the right, so let the left side be the variable side.<\/p>\n\n<table id=\"eip-id1168467377760\" style=\"width: 100%;\" summary=\"The first line says 7x equals negative x plus 24. The left side is labeled \u201cvariable side\u201d in red and the right side is labeled \u201cconstant side\u201d in red. The next line says \u201cRemove the negative x from the right side by adding x to both sides.\u201d Beside that is 7x plus a red x equals negative x plus a red x plus 24. The next line says \u201csimplify\u201d and shows 8x equals 24. The following line says \u201cAll the variables are on the left and the constants are on the right. Divide both sides by 8.\u201d Beside that is 8x over a red 8 equals 24 over a red 8. The next line says \u201csimplify\u201d and shows x equals 3. The next line says \u201ccheck\u201d and shows 7x equals negative x plus 24. Below that is \u201cSubstitute x equals 3\u201d and shows 7 times a red 3, equal sign with a question mark, negative red 3 plus 24. The last line says 21 equals 21.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467238229\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Remove the \\(-x\\) from the right side by adding \\(x\\) to both sides.<\/td>\n<td><span id=\"eip-id1168467263067\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467359022\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>All the variables are on the left and the constants are on the right. Divide both sides by 8.<\/td>\n<td><span id=\"eip-id1168468713840\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467311311\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute \\(x=3\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168465131873\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494586231\" data-type=\"problem\">\n<p id=\"fs-id1948298\">Solve: \\(12j=-4j+32\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1524724\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166490806219\"><em data-effect=\"italics\">j<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482688714\" data-type=\"problem\">\n\nSolve: \\(8h=-4h+12\\).\n\n<\/div>\n<div id=\"fs-id590470\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1355386\"><em data-effect=\"italics\">h<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations with Variables and Constants on Both Sides<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1244059\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1767277\">The next example will be the first to have variables <em data-effect=\"italics\">and<\/em> constants on both sides of the equation. As we did before, we\u2019ll collect the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> terms to one side and the <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> to the other side.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497196207\" data-type=\"problem\">\n\nSolve: \\(7x+5=6x+2\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166484059766\" data-type=\"solution\">\n\nStart by choosing which side will be the variable side and which side will be the constant side. The variable terms are \\(7x\\) and \\(6x\\). Since \\(7\\) is greater than \\(6\\), make the left side the variable side and so the right side will be the constant side.\n<table id=\"eip-id1168468709344\" style=\"width: 100%;\" summary=\"The first line says 7x plus 5 equals 6x plus 2. The next line says \u201cCollect the variable terms to the left side by subtracting 6x from both sides.\u201d Beside that is 7x minus a red 6x plus 5 equals 6x minus a red 6x plus 2. The next line says \u201cCombine like terms\u201d and shows x plus 5 equals 2. The next line says \u201cNow, collect the constants to the right side by subtracting 5 from both sides.\u201d Beside that is x plus 5 minus a red 5 equals 2 minus a red 5. The next line says \u201cSimplify\u201d and shows x equals negative 3. The next line says \u201cThe solution is x equals negative 3.\u201d The last step says \u201cCheck: Let x equal negative 3.\u201d Beside that is 7x plus 5 equals 6x plus 2. The next line says 7 times a red negative 3 plus 5, equal sign with a question mark, 6 times a red negative 3 plus 2. Below that is negative 21 plus 5, equal sign with a question mark, negative 18 plus 2. The last line says negative 16 equals negative 16.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468537221\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the variable terms to the left side by subtracting \\(6x\\) from both sides.<\/td>\n<td><span id=\"eip-id1168467429656\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467338898\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Now, collect the constants to the right side by subtracting 5 from both sides.<\/td>\n<td><span id=\"eip-id1168467330763\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467330780\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution is \\(x=-3\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=-3\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468571132\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1397980\" data-type=\"problem\">\n<p id=\"fs-id1359684\">Solve: \\(12x+8=6x+2\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary><em data-effect=\"italics\">x<\/em> = \u22121\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1357188\" data-type=\"problem\">\n<p id=\"fs-id1692853\">Solve: \\(9y+4=7y+12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1469991\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1249270\"><em data-effect=\"italics\">y<\/em> = 4<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1763313\">We\u2019ll summarize the steps we took so you can easily refer to them.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Solve an Equation with Variables and Constants on Both Sides<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168468371331\" class=\"stepwise\" type=\"1\">\n \t<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\n \t<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Make the coefficient of the variable \\(1\\), using the Multiplication or Division Property of Equality.<\/li>\n \t<li>Check the solution by substituting it into the original equation.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1166484081154\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n\nIt is a good idea to make the variable side the one in which the variable has the larger coefficient. This usually makes the arithmetic easier.\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1486587\" data-type=\"problem\">\n<p id=\"fs-id1332952\">Solve: \\(6n-2=-3n+7\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166482443035\" data-type=\"solution\">\n<p id=\"fs-id1166493771208\">We have \\(6n\\) on the left and \\(-3n\\) on the right. Since \\(6\\) &gt; \\(-3\\), make the left side the \u201cvariable\u201d side.<\/p>\n\n<table id=\"eip-id1168467335489\" style=\"width: 100%;\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \u201cWe don't want variables on the right side - add 3n to both sides to leave only constants on the right. Beside that is 6n plus a red 3n minus 2 equals negative 3n plus a red 3n plus 7. The next line says \u201cCombine like terms\u201d and shows 9n minus 2 equals 7. The next line says \u201cWe don't want any constants on the left side, so add 2 to both sides.\u201d Beside that is 9n minus 2 plus a red 2 equals 7 plus a red 2. The next line says \u201cSimplify\u201d and shows 9n equals 9. The next line says \u201cThe variable term is on the left and the constant term is on the right. To get the coefficient of n to be one, divide both sides by 9. Beside that is 9n over a red 9 equals 9 over a red 9. The next line says \u201cSimplify\u201d and shows n equals 1. The next line says \u201cCheck\u201d and shows 6n minus 2 equals negative 3n plus 7. Below that is \u201cSubstitute 1 for n\u201d and 6 times a red 1 minus 2 followed by an equal sign with a question mark, then negative 3 times a red 1 plus 7. The last line says 4 equals 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469614901\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We don't want variables on the right side\u2014add \\(3n\\) to both sides to leave only constants on the right.<\/td>\n<td><span id=\"eip-id1168469574727\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168466072161\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We don't want any constants on the left side, so add 2 to both sides.<\/td>\n<td><span id=\"eip-id1168469616858\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469468579\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The variable term is on the left and the constant term is on the right.\nTo get the coefficient of \\(n\\) to be one, divide both sides by 9.<\/td>\n<td><span id=\"eip-id1168469617677\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469613794\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute 1 for \\(n\\).<\/td>\n<td><span id=\"eip-id1168469485471\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482410079\" data-type=\"problem\">\n<p id=\"fs-id1481548\">Solve: \\(8q-5=-4q+7\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1945999\"><em data-effect=\"italics\">q<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492887225\">Solve: \\(7n-3=n+3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166493762183\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1741775\"><em data-effect=\"italics\">n<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166495279643\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1953082\" data-type=\"exercise\">\n<div id=\"fs-id1166482410079\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1857913\" data-type=\"problem\">\n<p id=\"fs-id1445284\">Solve: \\(2a-7=5a+8\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492881878\" data-type=\"solution\">\n\nThis equation has \\(2a\\) on the left and \\(5a\\) on the right. Since \\(5\\) &gt; \\(2\\), make the right side the variable side and the left side the constant side.\n<table id=\"eip-id1168466004451\" style=\"width: 100%;\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \u201cWe don't want variables on the right side - add 3n to both sides to leave only constants on the right. Beside that is 6n plus a red 3n minus 2 equals negative 3n plus a red 3n plus 7. The next line says \u201cCombine like terms\u201d and shows 9n minus 2 equals 7. The next line says \u201cWe don't want any constants on the left side, so add 2 to both sides.\u201d Beside that is 9n minus 2 plus a red 2 equals 7 plus a red 2. The next line says \u201cSimplify\u201d and shows 9n equals 9. The next line says \u201cThe variable term is on the left and the constant term is on the right. To get the coefficient of n to be one, divide both sides by 9. Beside that is 9n over a red 9 equals 9 over a red 9. The next line says \u201cSimplify\u201d and shows n equals 1. The next line says \u201cCheck\u201d and shows 6n minus 2 equals negative 3n plus 7. Below that is \u201cSubstitute 1 for n\u201d and 6 times a red 1 minus 2 followed by an equal sign with a question mark, then negative 3 times a red 1 plus 7. The last line says 4 equals 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469497825\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(2a\\) from both sides to remove the variable term from the left.<\/td>\n<td><span id=\"eip-id1168469353933\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469353950\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 8 from both sides to remove the constant from the right.<\/td>\n<td><span id=\"eip-id1168469805558\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466269006\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 3 to make 1 the coefficient of \\(a\\).<\/td>\n<td><span id=\"eip-id1168466048053\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466113284\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(a=-5\\).<\/td>\n<td><span id=\"eip-id1168469686306\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1458532\">Note that we could have made the left side the variable side instead of the right side, but it would have led to a negative coefficient on the variable term. While we could work with the negative, there is less chance of error when working with positives. The strategy outlined above helps avoid the negatives!<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497443661\" data-type=\"problem\">\n<p id=\"fs-id1498474\">Solve: \\(2a-2=6a+18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1573469\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary><em data-effect=\"italics\">a<\/em> = \u22125\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1476865\" data-type=\"problem\">\n<p id=\"fs-id1547301\">Solve: \\(4k-1=7k+17\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1956097\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490837958\"><em data-effect=\"italics\">k<\/em> = \u22126<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nTo solve an equation with fractions, we still follow the same steps to get the solution.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491053390\" data-type=\"problem\">\n<p id=\"fs-id1166490838129\">Solve: \\(\\frac{3}{2}\\phantom{\\rule{0.1em}{0ex}}x+5=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x-3\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1742076\" data-type=\"solution\">\n<p id=\"fs-id1166491054296\">Since \\(\\frac{3}{2}\\) &gt; \\(\\frac{1}{2}\\), make the left side the variable side and the right side the constant side.<\/p>\n\n<table id=\"eip-id1168469779179\" style=\"width: 100%;\" summary=\"The first line says three-halves x plus 5 equals one-half x minus 3. The next line says, \u201cSubtract one-half x from both sides,\u201d and shows three-halves x minus a red one-half x plus 5 equals one-half x minus a red one-half x minus 3. The next line says, \u201cCombine like terms,\u201d and shows x plus 5 equals negative 3. The next line says, \u201cSubtract 5 from both sides,\u201d and shows x plus 5 minus a red 5 equals negative 3 minus a red 5. The next line says, \u201cSimplify,\u201d and shows x equals negative 8. The last step says, \u201cCheck: Let x equal negative 8.\u201d Beside that is three-halves x plus 5 equals one-half x minus 3. Below that is three-halves times a red negative 8 plus 5 equals one-half times a red negative 8 minus 3. The next line shows negative 12 plus 5 equals negative 4 minus 3. The last line shows negative 7 equals negative 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467544617\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(\\frac{1}{2}x\\) from both sides.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168468496654\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467366826\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467366844\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168468743331\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=-8\\).<\/td>\n<td><span id=\"eip-id1168468350715\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493276476\" data-type=\"problem\">\n<p id=\"fs-id1166497276823\">Solve: \\(\\frac{7}{8}\\phantom{\\rule{0.1em}{0ex}}x-12=-\\frac{1}{8}\\phantom{\\rule{0.1em}{0ex}}x-2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166494721481\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166497294974\"><em data-effect=\"italics\">x<\/em> = 10<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491270654\" data-type=\"problem\">\n<p id=\"fs-id1166497354048\">Solve: \\(\\frac{7}{6}\\phantom{\\rule{0.1em}{0ex}}y+11=\\frac{1}{6}\\phantom{\\rule{0.1em}{0ex}}y+8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1436738\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166491248892\"><em data-effect=\"italics\">y<\/em> = \u22123<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166498082088\">We follow the same steps when the equation has decimals, too.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490863127\" data-type=\"problem\">\n\nSolve: \\(3.4x+4=1.6x-5\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1517936\" data-type=\"solution\">\n<p id=\"fs-id1166490904889\">Since \\(3.4\\) &gt; \\(1.6\\), make the left side the variable side and the right side the constant side.<\/p>\n\n<table id=\"eip-id1168466001051\" style=\"width: 100%;\" summary=\"The top line says 3.4x plus 4 equals 1.6x minus 5. The next line says, \u201cSubtract 1.6x from both sides,\u201d and shows 3.4x minus a red 1.6x plus 4 equals 1.6x minus a red 1.6x minus 5. The next line says, \u201cCombine like terms,\u201d and shows 1.8x plus 4 equals negative 5. The next line says, \u201cSubtract 4 from both sides,\u201d and shows 1.8x plus 4 minus a red 4 equals negative 5 minus a red 4. The next line says, \u201cSimplify,\u201d and shows 1.8x equals negative 9. The next line says, \u201cUse the division property of equality,\u201d and shows 1.8x over a red 1.8 equals negative 9 over a red 1.8. The next line says, \u201cSimplify,\u201d and shows x equals negative 5. The last step says, \u201cCheck: Substitute x equals negative 5.\u201d Beside that is 3.4x plus 4 equals 1.6x minus 5. Below that is 3.4 times a red negative 5 plus 4 equals 1.6 times a red negative 5 minus 5. Below that is negative 17 plus 4 equals negative 8 minus 5. The last line shows negative 13 equals negative 13.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469879099\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(1.6x\\) from both sides.<\/td>\n<td><span id=\"eip-id1168466657795\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168466657811\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 4 from both sides.<\/td>\n<td><span id=\"eip-id1168469616764\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469617706\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Division Property of Equality.<\/td>\n<td><span id=\"eip-id1168469692083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469747571\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=-5\\).<\/td>\n<td><span id=\"eip-id1168469461335\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490838002\" data-type=\"problem\">\n<p id=\"fs-id1166493760978\">Solve: \\(2.8x+12=-1.4x-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1329708\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166479093904\"><em data-effect=\"italics\">x<\/em> = \u22125<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497359897\" data-type=\"problem\">\n<p id=\"fs-id1945758\">Solve: \\(3.6y+8=1.2y-4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166479038932\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1833479\"><em data-effect=\"italics\">y<\/em> = \u22125<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations Using a General Strategy<\/h1>\n<\/div>\n<div id=\"fs-id1166492018062\" class=\"bc-section section\" data-depth=\"1\">\n\nEach of the first few sections of this chapter has dealt with solving one specific form of a <span class=\"no-emphasis\" data-type=\"term\">linear equation<\/span>. It\u2019s time now to lay out an overall strategy that can be used to solve <em data-effect=\"italics\">any<\/em> linear equation. We call this the <em data-effect=\"italics\">general strategy<\/em>. Some equations won\u2019t require all the steps to solve, but many will. Simplifying each side of the equation as much as possible first makes the rest of the steps easier.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Use a General Strategy for Solving Linear Equations<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168467248588\" class=\"stepwise\" type=\"1\">\n \t<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\n \t<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Make the coefficient of the variable term to equal to \\(1\\). Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\n \t<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1445020\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1510057\" data-type=\"problem\">\n<p id=\"fs-id1392091\">Solve: \\(3\\left(x+2\\right)=18\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168468387403\" style=\"width: 100%;\" summary=\"Simplify each side of the equation as much as possible. Use the Distributive Property.\u201d Beside that is 3 times parentheses x plus 2 equals 18. The next line says, \u201cCollect all variable terms on one side of the equation - all xs are already on the left side.\u201d Beside that is 3x plus 6 equals 18. The next line says, \u201cCollect constant terms on the other side of the equation. Subtract 6 from each side.\u201d Beside that is 3x plus 6 minus a red 6 equals 18 minus a red 6. The next line says, \u201cSimplify,\u201d and shows 3x equals 12. The next line says, \u201cMake the coefficient of the variable term to equal 1. Divide each side by 3.\u201d Beside that is 3x over a red 3 equals 12 over a red 3. The next line says, \u201cSimplify,\u201d and shows x equals 4. The last step says, \u201cCheck the solution. Let x equal 4.\u201d Below that is 3 times parentheses x plus 2 equals 18. Below that is 3 times parentheses red 4 plus 2, equal sign with a question mark, 18. Below that is 3 times 6, equal sign with a question mark, 18. The last line shows 18 equals 18 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1187288\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side of the equation as much as possible.\nUse the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468533951\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect all variable terms on one side of the equation\u2014all \\(x\\)s are already on the left side.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Collect constant terms on the other side of the equation.\nSubtract 6 from each side<\/td>\n<td><span id=\"eip-id1168467248487\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468721440\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Make the coefficient of the variable term equal to 1. Divide each side by 3.<\/td>\n<td><span id=\"eip-id1168468646687\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468646704\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=4\\).<\/td>\n<td><span id=\"eip-id1168465131755\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1735280\" data-type=\"problem\">\n\nSolve: \\(5\\left(x+3\\right)=35\\).\n\n<\/div>\n<div id=\"fs-id1202244\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary><em data-effect=\"italics\">x<\/em> = 4\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1367765\">Solve: \\(6\\left(y-4\\right)=-18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166484109032\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1431126\"><em data-effect=\"italics\">y<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1258354\" data-type=\"problem\">\n<p id=\"fs-id1285644\">Solve: \\(-\\left(x+5\\right)=7\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469659755\" style=\"width: 100%; height: 363px;\" summary=\"Simplify each side of the equation as much as possible by distributing. The only x term is on the left side, so all variable terms are on the left side of the equation.\u201d Beside that is negative x minus 5 equals 7. The next line says, \u201cAdd 5 to both sides to get all constant terms on the right side of the equation.\u201d Beside that is negative x minus 5 plus a red 5 equals 7 plus a red 5. The next line says, \u201cSimplify,\u201d and shows negative x equals 12. The next line says, \u201cMake the coefficient of the variable term equal to 1 by multiplying both sides by negative 1.\u201d Beside that is a red negative 1 times negative x equals a red negative 1 times 12. The next line says, \u201cSimplify,\u201d and shows x equals negative 12. The last step says, \u201cCheck: Let x equal negative 12.\u201d Beside that is negative parentheses x plus 5 equals 7, then negative parentheses red negative 12 plus 5 equals 7, then negative negative 7 equals 7, then 7 equals 7.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><\/td>\n<td style=\"height: 24px;\"><span id=\"eip-id1168466183184\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px;\">Simplify each side of the equation as much as possible by distributing.\nThe only \\(x\\) term is on the left side, so all variable terms are on the left side of the equation.<\/td>\n<td style=\"height: 33px;\"><span id=\"eip-id1168466110663\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Add 5 to both sides to get all constant terms on the right side of the equation.<\/td>\n<td style=\"height: 28px;\"><span id=\"eip-id1168469735440\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Simplify.<\/td>\n<td style=\"height: 28px;\"><span id=\"eip-id1168466091761\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px;\">Make the coefficient of the variable term equal to 1 by multiplying both sides by -1.<\/td>\n<td style=\"height: 26px;\"><span id=\"eip-id1168466322456\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\">Simplify.<\/td>\n<td style=\"height: 24px;\"><span id=\"eip-id1168469798411\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 134px;\">\n<td style=\"height: 134px;\">Check: Let \\(x=-12\\).<\/td>\n<td style=\"height: 134px;\"><span id=\"eip-id1168048774145\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168048774155\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168048774165\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168048774174\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1685205\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1479602\" data-type=\"exercise\">\n<div id=\"fs-id1166484109032\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492696720\" data-type=\"problem\">\n\nSolve: \\(-\\left(y+8\\right)=-2\\).\n\n<\/div>\n<div id=\"fs-id1729772\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166479011445\"><em data-effect=\"italics\">y<\/em> = \u22126<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166494736971\">Solve: \\(-\\left(z+4\\right)=-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1731591\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166494721814\"><em data-effect=\"italics\">z<\/em> = 8<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166491410544\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1166492696720\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1771048\" data-type=\"problem\">\n<p id=\"fs-id1166484125384\">Solve: \\(4\\left(x-2\\right)+5=-3\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469612809\" style=\"width: 100%;\" summary=\"The top line shows 4 times parentheses x minus 2 plus 5 equals negative 3. The next line says, \u201cSimplify each side of the equation as much as possible. Distribute.\u201d Beside that is 4x minus 8 plus 5 equals negative 3. The next line says, \u201cCombine like terms,\u201d and shows 4x minus 3 equals negative 3. The next line says, \u201cThe only x is on the left side, so all variable terms are on one side of the equation. Add 3 to both sides to get all constant terms on the other side of the equation.\u201d Beside that is 4x minus 3 plus a red 3 equals negative 3 plus a red 3. The next line says, \u201cSimplify,\u201d and shows 4x equals 0. The next line says, \u201cMake the coefficient of the variable term to equal to 1 by dividing both sides by 4.\u201d Beside that is 4x over a red 4 equals 0 over a red 4. The next line says, \u201cSimplify,\u201d and shows x equals 0. The last step says, \u201cCheck: Let x equal 0.\u201d Beside that is 4 times parentheses x minus 2 plus 5 equals negative 3. The next line says 4 times parentheses red 0 minus 2 plus 5 equals negative 3. Below that is 4 times negative 2 plus 5 equals negative 3, then negative 8 plus 5 equals negative 3, then negative 3 equals negative 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469614509\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side of the equation as much as possible.\nDistribute.<\/td>\n<td><span id=\"eip-id1168466081811\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms<\/td>\n<td><span id=\"eip-id1168466174407\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The only \\(x\\) is on the left side, so all variable terms are on one side of the equation.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add 3 to both sides to get all constant terms on the other side of the equation.<\/td>\n<td><span id=\"eip-id1168466034680\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469615730\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Make the coefficient of the variable term equal to 1 by dividing both sides by 4.<\/td>\n<td><span id=\"eip-id1168465988158\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469839767\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=0\\).<\/td>\n<td><span id=\"eip-id1168469773952\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1869700\">Solve: \\(2\\left(a-4\\right)+3=-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166493760882\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166493485396\"><em data-effect=\"italics\">a<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1417482\" data-type=\"problem\">\n<p id=\"fs-id1166488299701\">Solve: \\(7\\left(n-3\\right)-8=-15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166482135584\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1538857\"><em data-effect=\"italics\">n<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1502246\" data-type=\"problem\">\n\nSolve: \\(8-2\\left(3y+5\\right)=0\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n\nBe careful when distributing the negative.\n<table id=\"eip-id1168467174932\" style=\"width: 100%;\" summary=\"The top line says 8 minus 2 parentheses 3y plus 5 equals 0. The next line says, \u201cSimplify - use the Distributive Property,\u201d and shows 8 minus 6y minus 10 equals 0. The next line says, \u201cCombine like terms,\u201d and shows negative 6y minus 2 equals 0. The next line says, \u201cAdd 2 to both sides to collect constants on the right,\u201d and shows negative 6y minus 2 plus a red 2 equals 0 plus a red 2. The next line says, \u201cSimplify,\u201d and shows negative 6y equals 2. The next line says, \u201cDivide both sides by negative 6,\u201d and shows negative 6y over a red negative 6 equals 2 over a red negative 6. The following line says, \u201cSimplify,\u201d and shows y equals negative one-third. The last step says, \u201cCheck: let y equal negative one-third.\u201d Beside that is the original equation. Below that is 8 minus 2 parentheses 3 times a red negative one-third plus 5 equals 0. Below is 8 minus 2 parentheses negative 1 plus 5 equals 0, then 8 minus 2 times 4 equals 0, then 8 minus 8 equals 0, and then 0 equals 0.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467359014\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014use the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468376858\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168468567044\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 2 to both sides to collect constants on the right.<\/td>\n<td><span id=\"eip-id1168468567060\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467473445\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by \u22126.<\/td>\n<td><span id=\"eip-id1168467148757\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467148774\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(y=-\\frac{1}{3}\\).<\/td>\n<td><span id=\"eip-id1168467174781\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1482353\" data-type=\"problem\">\n<p id=\"fs-id1166494737529\">Solve: \\(12-3\\left(4j+3\\right)=-17\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\\(j=\\frac{5}{3}\\)\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1361205\">Solve: \\(-6-8\\left(k-2\\right)=-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1271847\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1732922\">\\(k=\\frac{5}{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1476001\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nSolve: \\(3\\left(x-2\\right)-5=4\\left(2x+1\\right)+5\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1218520\" data-type=\"solution\">\n<table id=\"eip-id1168468704060\" style=\"width: 100%;\" summary=\"The top line says 3 parentheses x minus 2 minus 5 equals 4 parentheses 2x plus 1 plus 5. The next line says, \u201cDistribute,\u201d and shows 3x minus 6 minus 5 equals 8x plus 4 plus 5. The next line says, \u201cCombine like terms,\u201d and shows 3x minus 11 equals 8x plus 9. The next line says \u201cSubtract 3x to get all the variables on the right since 8 is greater than 3,\u201d and shows 3x minus a red 3x minus 11 equals 8x minus a red 3x plus 9. The next line says, \u201cSimplify,\u201d and shows negative 11 equals 5x plus 9. The next line says, \u201cSubtract 9 to get the constants on the left,\u201d and shows negative 11 minus a red 9 equals 5x plus 9 minus a red 9. The net line says, \u201cSimplify,\u201d and shows negative 20 equals 5x. The next line says, \u201cDivide by 5,\u201d and shows negative 20 over a red 5 equals 5x over a red 5. The next line says, \u201cSimplify,\u201d and shows negative 4 equals x. The last step says, \u201cCheck. Substitute x equals negative 4.\u201d Beside this is the original equation, followed by 3 times parentheses red negative 4 minus 2 minus 5 equals 4 times parentheses 2 times negative 4 plus 1 plus 5. Below that is 3 times negative 6 minus 5 equals 4 times parentheses negative 8 plus 1 plus 5. Below that is negative 18 minus 5 equals 4 times negative 7 plus 5. Below that is negative 23 equals negative 28 plus 5. The last line shows negative 23 equals negative 23.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466230669\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469522784\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168465986112\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(3x\\) to get all the variables on the right since \\(8\\) &gt; \\(3\\).<\/td>\n<td><span id=\"eip-id1168466281124\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469801111\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 9 to get the constants on the left.<\/td>\n<td><span id=\"eip-id1168466036190\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466215053\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 5.<\/td>\n<td><span id=\"eip-id1168466267864\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466026625\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute: \\(-4=x\\).<\/td>\n<td><span id=\"eip-id1168466463596\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1453989\" data-type=\"problem\">\n<p id=\"fs-id1341235\">Solve: \\(6\\left(p-3\\right)-7=5\\left(4p+3\\right)-12\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490921468\"><em data-effect=\"italics\">p<\/em> = \u22122<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166484083199\" data-type=\"problem\">\n<p id=\"fs-id1948566\">Solve: \\(8\\left(q+1\\right)-5=3\\left(2q-4\\right)-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1324992\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1869648\"><em data-effect=\"italics\">q<\/em> = \u22128<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492690992\" data-type=\"problem\">\n<p id=\"fs-id1482586\">Solve: \\(\\frac{1}{2}\\left(6x-2\\right)=5-x\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469851853\" style=\"width: 100%;\" summary=\"The top line says one-half times parentheses 6x minus 2 equals 5 minus x. The next line says, \u201cDistribute,\u201d and shows 3x minus 1 equals 5 minus x. The next line says, \u201cAdd x to get all the variables on the left,\u201d and shows 3x minus 1 plus a red x equals 5 minus x plus a red x. The next line says, \u201cSimplify,\u201d and shows 4x minus 1 equals 5. The next line says, \u201cAdd 1 to get constants on the right,\u201d and shows 4x minus 1 plus a red 1 equals 5 plus a red 1. The next line says, \u201cSimplify,\u201d and shows 4x equals 6. The next line says, \u201cDivide by 4,\u201d and shows 4x over a red 4 equals 6 over a red 4. The next line says, \u201cSimplify,\u201d and shows x equals three-halves. The last step says, \u201cCheck: Let x equal three-halves.\u201d Beside that is the original equation followed by one-half times parentheses 6 times a red three-halves minus 2 equals 5 minus a red three-halves. Below that is one-half times parentheses 9 minus 2 equals ten-halves minus three-halves, then one-half times 7 equals 7 halves, then 7 halves equals 7 halves.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466324380\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168465998394\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add \\(x\\) to get all the variables on the left.<\/td>\n<td><span id=\"eip-id1168466204103\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466661049\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 1 to get constants on the right.<\/td>\n<td><span id=\"eip-id1168469456166\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469577022\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 4.<\/td>\n<td><span id=\"eip-id1168466121572\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466166059\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=\\frac{3}{2}\\).<\/td>\n<td><span id=\"eip-id1168466426974\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493761572\" data-type=\"problem\">\n<p id=\"fs-id1166493721820\">Solve: \\(\\frac{1}{3}\\left(6u+3\\right)=7-u\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166492013626\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1704714\"><em data-effect=\"italics\">u<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1361128\" data-type=\"problem\">\n<p id=\"fs-id1166491409253\">Solve: \\(\\frac{2}{3}\\left(9x-12\\right)=8+2x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166497359267\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490773708\"><em data-effect=\"italics\">x<\/em> = 4<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nIn many applications, we will have to solve equations with decimals. The same general strategy will work for these equations.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491403013\" data-type=\"problem\">\n<p id=\"fs-id1486914\">Solve: \\(0.24\\left(100x+5\\right)=0.4\\left(30x+15\\right)\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1449046\" data-type=\"solution\">\n<table id=\"eip-id1168468569426\" style=\"width: 100%;\" summary=\"The top line says 0.24 times parentheses 100x plus 5 equals 0.4 times parentheses 30x plus 15. The next line says, \u201cDistribute,\u201d and shows 24x plus 1.2 equals 12x plus 6. The next line says, \u201cSubtract 12x to get the xs to the left,\u201d and shows 24x plus 1.2 minus a red 12x equals 12x plus 6 minus a red 12x. The next line says, \u201cSimplify,\u201d and shows 12x plus 1.2 equals 6. The next line says, \u201cSubtract 1.2 to get the constants to the right,\u201d and shows 12x plus 1.2 minus a red 1.2 equals 6 minus a red 1.2. The next line says, \u201cSimplify,\u201d and shows 12x equals 4.8. The next line says, \u201cDivide,\u201d and shows 12x over a red 12 equals 4.8 over a red 12. The next line says, \u201cSimplify,\u201d and shows x equals 0.4. The next line says, \u201cCheck,\u201d and shows the original equation. Below that, it says, \u201cLet x equal 0.4,\u201d and shows 0.24 times parentheses 100 times a red 0.4 plus 5, equal sign with a question mark, 0.4 times parentheses 30 times a red 0.4 plus 15. Below that is 0.24 times parentheses 40 plus 5, equal sign with a question mark, 0.4 times parentheses 12 plus 15. Below that is 0.24 times 45, equal sign with a question mark, 0.4 times 27. The last line says 10.8 equals 10.8 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469856402\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469683989\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(12x\\) to get all the \\(x\\)s to the left.<\/td>\n<td><span id=\"eip-id1168466144870\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469868305\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 1.2 to get the constants to the right.<\/td>\n<td><span id=\"eip-id1168469491155\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469594198\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1168469544803\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469829057\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=0.4\\).<\/td>\n<td><span id=\"eip-id1168466203358\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497435575\" data-type=\"problem\">\n<p id=\"fs-id1296459\">Solve: \\(0.55\\left(100n+8\\right)=0.6\\left(85n+14\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1789082\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166488297923\">1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1542714\" data-type=\"problem\">\n<p id=\"fs-id1166491412269\">Solve: \\(0.15\\left(40m-120\\right)=0.5\\left(60m+12\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1460794\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166494770264\">\u22121<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"eip-578\">\n \t<li><strong>Solve an equation with variables and constants on both sides<\/strong>\n<ol id=\"eip-id1170322988380\" class=\"stepwise\" type=\"1\">\n \t<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\n \t<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Make the coefficient of the variable 1, using the Multiplication or Division Property of Equality.<\/li>\n \t<li>Check the solution by substituting into the original equation.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong>General strategy for solving linear equations<\/strong>\n<ol id=\"eip-id1170324010914\" class=\"stepwise\" type=\"1\">\n \t<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\n \t<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Make the coefficient of the variable term to equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\n \t<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<div id=\"fs-id1166490790567\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1681739\" data-type=\"exercise\">\n<h1 id=\"fs-id1166497435575\" data-type=\"problem\">Practice Makes Perfect<\/h1>\n<div id=\"fs-id1366050\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1807401\">Solve an Equation with Constants on Both Sides<\/h2>\n<p id=\"eip-16\">In the following exercises, solve the equation for the variable.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>1. \\(7x-8=34\\)<\/td>\n<td>2. \\(6x-2=40\\)<\/td>\n<\/tr>\n<tr>\n<td>3. \\(14y+7=91\\)<\/td>\n<td>4. \\(11w+6=93\\)<\/td>\n<\/tr>\n<tr>\n<td>5. \\(4m+9=-23\\)<\/td>\n<td>6. \\(3a+8=-46\\)<\/td>\n<\/tr>\n<tr>\n<td>7. \\(-47=6b+1\\)<\/td>\n<td>8. \\(-50=7n-1\\)<\/td>\n<\/tr>\n<tr>\n<td>9. \\(29=-8x-3\\)<\/td>\n<td>10. \\(25=-9y+7\\)<\/td>\n<\/tr>\n<tr>\n<td>11. \\(-14\\text{q}-15=13\\)<\/td>\n<td>12. \\(-12p-3=15\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1494639\">Solve an Equation with Variables on Both Sides<\/h2>\n<p id=\"eip-57\">In the following exercises, solve the equation for the variable.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>13. \\(9k=8k-11\\)<\/td>\n<td>14. \\(8z=7z-7\\)<\/td>\n<\/tr>\n<tr>\n<td>15. \\(6x+27=9x\\)<\/td>\n<td>16. \\(4x+36=10x\\)<\/td>\n<\/tr>\n<tr>\n<td>17. \\(b=-4b-15\\)<\/td>\n<td>18. \\(c=-3c-20\\)<\/td>\n<\/tr>\n<tr>\n<td>19. \\(7z=39-6z\\)<\/td>\n<td>20. \\(5q=44-6q\\)<\/td>\n<\/tr>\n<tr>\n<td>21. \\(8x+\\frac{3}{4}=7x\\)<\/td>\n<td>22. \\(3y+\\frac{1}{2}=2y\\)<\/td>\n<\/tr>\n<tr>\n<td>23. \\(-15r-8=-11r\\)<\/td>\n<td>24. \\(-12a-8=-16a\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166490741372\">Solve an Equation with Variables and Constants on Both Sides<\/h2>\n<p id=\"eip-969\">In the following exercises, solve the equations for the variable.<\/p>\n\n<table border=\"0\">\n<tbody>\n<tr>\n<td>25. \\(4x-17=3x+2\\)<\/td>\n<td>26. \\(6x-15=5x+3\\)<\/td>\n<\/tr>\n<tr>\n<td>27. \\(21+6f=7f+14\\)<\/td>\n<td>28. \\(26+8d=9d+11\\)<\/td>\n<\/tr>\n<tr>\n<td>29. \\(8q-5=5q-20\\)<\/td>\n<td>30. \\(3p-1=5p-33\\)<\/td>\n<\/tr>\n<tr>\n<td>31. \\(9c+7=-2c-37\\)<\/td>\n<td>32. \\(4a+5=-a-40\\)<\/td>\n<\/tr>\n<tr>\n<td>33. \\(12x-17=-3x+13\\)<\/td>\n<td>34. \\(8y-30=-2y+30\\)<\/td>\n<\/tr>\n<tr>\n<td>35. \\(3y-4=12-y\\)<\/td>\n<td>36. \\(2\\text{z}-4=23-\\text{z}\\)<\/td>\n<\/tr>\n<tr>\n<td>37. \\(\\frac{4}{3}\\phantom{\\rule{0.1em}{0ex}}m-7=\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}m-13\\)<\/td>\n<td>38. \\(\\frac{5}{4}\\phantom{\\rule{0.1em}{0ex}}c-3=\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}c-16\\)<\/td>\n<\/tr>\n<tr>\n<td>39. \\(11-\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}a=\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}a+4\\)<\/td>\n<td>40. \\(8-\\frac{2}{5}\\phantom{\\rule{0.1em}{0ex}}q=\\frac{3}{5}\\phantom{\\rule{0.1em}{0ex}}q+6\\)<\/td>\n<\/tr>\n<tr>\n<td>41. \\(\\frac{5}{4}\\phantom{\\rule{0.1em}{0ex}}a+15=\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}a-5\\)<\/td>\n<td>42. \\(\\frac{4}{3}\\phantom{\\rule{0.1em}{0ex}}n+9=\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}n-9\\)<\/td>\n<\/tr>\n<tr>\n<td>43. \\(\\frac{3}{5}\\phantom{\\rule{0.1em}{0ex}}p+2=\\frac{4}{5}\\phantom{\\rule{0.1em}{0ex}}p-1\\)<\/td>\n<td>44. \\(\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}y+7=\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}y-3\\)<\/td>\n<\/tr>\n<tr>\n<td>45. \\(13z+6.45=8z+23.75\\)<\/td>\n<td>46. \\(14n+8.25=9n+19.60\\)<\/td>\n<\/tr>\n<tr>\n<td>47. \\(2.7w-80=1.2w+10\\)<\/td>\n<td>48. \\(2.4w-100=0.8w+28\\)<\/td>\n<\/tr>\n<tr>\n<td>49. \\(6.6x-18.9=3.4x+54.7\\)<\/td>\n<td>50. \\(5.6r+13.1=3.5r+57.2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1560582\">Solve an Equation Using the General Strategy<\/h2>\n<p id=\"eip-377\">In the following exercises, solve the linear equation using the general strategy.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>51. \\(4\\left(y+7\\right)=64\\)<\/td>\n<td>52. \\(5\\left(x+3\\right)=75\\)<\/td>\n<\/tr>\n<tr>\n<td>53. \\(9=3\\left(x-3\\right)\\)<\/td>\n<td>54. \\(8=4\\left(x-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>55. \\(14\\left(y-6\\right)=-42\\)<\/td>\n<td>56. \\(20\\left(y-8\\right)=-60\\)<\/td>\n<\/tr>\n<tr>\n<td>57. \\(-7\\left(3n+4\\right)=14\\)<\/td>\n<td>58. \\(-4\\left(2n+1\\right)=16\\)<\/td>\n<\/tr>\n<tr>\n<td>59. \\(8\\left(3+3\\text{p}\\right)=0\\)<\/td>\n<td>60. \\(3\\left(10+5r\\right)=0\\)<\/td>\n<\/tr>\n<tr>\n<td>61. \\(\\frac{3}{5}\\left(10x-5\\right)=27\\)<\/td>\n<td>62. \\(\\frac{2}{3}\\left(9c-3\\right)=22\\)<\/td>\n<\/tr>\n<tr>\n<td>63. \\(4\\left(2.5v-0.6\\right)=7.6\\)<\/td>\n<td>64. \\(5\\left(1.2u-4.8\\right)=-12\\)<\/td>\n<\/tr>\n<tr>\n<td>65. \\(0.5\\left(16m+34\\right)=-15\\)<\/td>\n<td>66. \\(0.2\\left(30n+50\\right)=28\\)<\/td>\n<\/tr>\n<tr>\n<td>67. \\(-\\left(t-8\\right)=17\\)<\/td>\n<td>68. \\(-\\left(w-6\\right)=24\\)<\/td>\n<\/tr>\n<tr>\n<td>69. \\(8\\left(6b-7\\right)+23=63\\)<\/td>\n<td>70. \\(9\\left(3a+5\\right)+9=54\\)<\/td>\n<\/tr>\n<tr>\n<td>71. \\(13+2\\left(m-4\\right)=17\\)<\/td>\n<td>72. \\(10+3\\left(z+4\\right)=19\\)<\/td>\n<\/tr>\n<tr>\n<td>73. \\(-9+6\\left(5-k\\right)=12\\)<\/td>\n<td>74. \\(7+5\\left(4-q\\right)=12\\)<\/td>\n<\/tr>\n<tr>\n<td>75. \\(18-\\left(9r+7\\right)=-16\\)<\/td>\n<td>76. \\(15-\\left(3r+8\\right)=28\\)<\/td>\n<\/tr>\n<tr>\n<td>77. \\(18-2\\left(y-3\\right)=32\\)<\/td>\n<td>78. \\(11-4\\left(y-8\\right)=43\\)<\/td>\n<\/tr>\n<tr>\n<td>79. \\(3\\left(4n-1\\right)-2=8n+3\\)<\/td>\n<td>80. \\(9\\left(p-1\\right)=6\\left(2p-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>81. \\(5\\left(x-4\\right)-4x=14\\)<\/td>\n<td>82. \\(9\\left(2m-3\\right)-8=4m+7\\)<\/td>\n<\/tr>\n<tr>\n<td>83. \\(5+6\\left(3s-5\\right)=-3+2\\left(8s-1\\right)\\)<\/td>\n<td>84. \\(8\\left(x-4\\right)-7x=14\\)<\/td>\n<\/tr>\n<tr>\n<td>85. \\(4\\left(x-1\\right)-8=6\\left(3x-2\\right)-7\\)<\/td>\n<td>86. \\(-12+8\\left(x-5\\right)=-4+3\\left(5x-2\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1732048\" class=\"everyday\" data-depth=\"2\">\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table border=\"0\">\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">Making a fence 87.\u00a0<\/strong> Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is \\(150\\) feet. The length is \\(15\\) feet more than the width. Find the width, \\(w\\), by solving the equation \\(150=2\\left(w+15\\right)+2w\\).<\/td>\n<td><strong data-effect=\"bold\">Concert tickets<\/strong>\u00a0 88. At a school concert, the total value of tickets sold was \\(\\text{\\$1,506.}\\) Student tickets sold for \\(\\text{\\$6}\\) and adult tickets sold for \\(\\text{\\$9.}\\) The number of adult tickets sold was \\(5\\) less than \\(3\\) times the number of student tickets. Find the number of student tickets sold, \\(s\\), by solving the equation \\(6s+9\\left(3s-5\\right)=1506\\).<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Coins<\/strong> 89. Rhonda has \\(\\text{\\$1.90}\\) in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, \\(n\\), by solving the equation \\(0.05n+0.10\\left(2n-1\\right)=1.90\\).<\/td>\n<td><strong data-effect=\"bold\">Fencing<\/strong> 90. Micah has \\(74\\) feet of fencing to make a rectangular dog pen in his yard. He wants the length to be \\(25\\) feet more than the width. Find the length, \\(L\\), by solving the equation \\(2L+2\\left(L-25\\right)=74\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166483068552\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<div id=\"fs-id1440481\" data-type=\"exercise\">\n<div id=\"fs-id1166491068825\" data-type=\"problem\">\n<table border=\"0\">\n<tbody>\n<tr>\n<td>91. 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?<\/td>\n<td>92. Solve the equation \\(10x+14=-2x+38\\), explaining all the steps of your solution.<\/td>\n<\/tr>\n<tr>\n<td>93. What is the first step you take when solving the equation \\(3-7\\left(y-4\\right)=38?\\) Explain why this is your first step.<\/td>\n<td>94. Solve the equation \\(\\frac{1}{4}\\left(8x+20\\right)=3x-4\\) explaining all the steps of your solution as in the examples in this section.<\/td>\n<\/tr>\n<tr>\n<td>95. Using your own words, list the steps in the General Strategy for Solving Linear Equations.<\/td>\n<td>96. 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.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div id=\"fs-id1166470615289\" data-type=\"exercise\">\n<div id=\"fs-id1166479431647\" data-type=\"problem\">\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>1. 6<\/td>\n<td>3.6<\/td>\n<td>5. -8<\/td>\n<\/tr>\n<tr>\n<td>7. -8<\/td>\n<td>9. -4<\/td>\n<td>11. -2<\/td>\n<\/tr>\n<tr>\n<td>13. -11<\/td>\n<td>15. 9<\/td>\n<td>17. -3<\/td>\n<\/tr>\n<tr>\n<td>19. 3<\/td>\n<td>21. -3\/4<\/td>\n<td>25. 19<\/td>\n<\/tr>\n<tr>\n<td>27. 7<\/td>\n<td>29. -5<\/td>\n<td>31. -4<\/td>\n<\/tr>\n<tr>\n<td>33. 2<\/td>\n<td>35. 4<\/td>\n<td>37. -6<\/td>\n<\/tr>\n<tr>\n<td>39. 7<\/td>\n<td>41. -40<\/td>\n<td>43. 15<\/td>\n<\/tr>\n<tr>\n<td>45. 3.46<\/td>\n<td>47. 60<\/td>\n<td>49. 23<\/td>\n<\/tr>\n<tr>\n<td>51. 9<\/td>\n<td>53. 6<\/td>\n<td>55. 3<\/td>\n<\/tr>\n<tr>\n<td>57. \u22122<\/td>\n<td>59. \u22121<\/td>\n<td>61. 5<\/td>\n<\/tr>\n<tr>\n<td>63. 0.52<\/td>\n<td>65. 0.25<\/td>\n<td>67. \u22129<\/td>\n<\/tr>\n<tr>\n<td>69. 2<\/td>\n<td>71. 6<\/td>\n<td>73. 3\/2<\/td>\n<\/tr>\n<tr>\n<td>75. 3<\/td>\n<td>77. \u22124<\/td>\n<td>79. 2<\/td>\n<\/tr>\n<tr>\n<td>81. 34<\/td>\n<td>83. 10<\/td>\n<td>85. 2<\/td>\n<\/tr>\n<tr>\n<td>87. 30 feet<\/td>\n<td>89. 8 nickels<\/td>\n<td>91. Answers will vary.<\/td>\n<\/tr>\n<tr>\n<td>93. Answers will vary.<\/td>\n<td>95. Answers will vary.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cSolve Equations with Variables and Constants on Both Sides\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Solve an equation with constants on both sides<\/li>\n<li>Solve an equation with variables on both sides<\/li>\n<li>Solve an equation with variables and constants on both sides<\/li>\n<li>Solve equations using a general strategy<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 id=\"fs-id1166497354586\" data-type=\"note\">Solve an Equation with Constants on Both Sides<\/h1>\n<div class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166491426623\">You may have noticed that in all the equations we have solved so far, all the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> terms were on only one side of the equation with the <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> on the other side. This does not happen all the time\u2014so now we\u2019ll see how to solve equations where the variable terms and\/or constant terms are on both sides of the equation.<\/p>\n<p id=\"fs-id1474518\">Our strategy will involve choosing one side of the equation to be the variable side, and the other side of the equation to be the constant side. Then, we will use the Subtraction and Addition Properties of Equality, step by step, to get all the variable terms together on one side of the equation and the constant terms together on the other side.<\/p>\n<p id=\"fs-id1166493722197\">By doing this, we will transform the equation that started with variables and constants on both sides into the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7856b2f32c5d9a89f37149c9ebb5e229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#120;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/>. We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494591529\" data-type=\"problem\">\n<p id=\"fs-id1166494722150\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-978846939848c634ebc97659076eccd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#54;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"105\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492789016\" data-type=\"solution\">\n<p id=\"fs-id1166484083743\">In this equation, the variable is only on the left side. It makes sense to call the left side the variable side. Therefore, the right side will be the constant side. We\u2019ll write the labels above the equation to help us remember what goes where.<\/p>\n<table id=\"eip-id1168467380704\" class=\"unnumbered unstyled\" summary=\"The top line says 4x plus 6 equals negative 14. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says, \u201cSince the left side is the variable side, the 6 is out of place. We must 'undo' adding 6 by subtracting 6, and to keep the equality we must subtract 6 from both sides. Use the Subtraction Property of Equality.\u201d Beside this is 4x plus 6 minus a red 6 equals negative 14 minus a red 6. The next line says \u201cSimplify\u201d and shows 4x equals negative 20. Below this, it says \u201cNow all the xs are on the left and the constant on the right.\u201d The next line says \u201cUse the Division Property of Equality\u201d and shows 4x over a red 4 equals negative 20 over a red 4. The next line says \u201cSimplify\u201d and shows x equals negative 5. The last step says \u201cCheck\u201d and shows 4x plus 6 equals negative 14. Below this is 4 times a red negative 5 plus 6, equal sign with a question mark, negative 14. Below is negative 20 plus 6, equal sign with a question mark, negative 14. The last line says negative 14 equals negative 14 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168467580178\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_03_039_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Since the left side is the variable side, the 6 is out of place. We must &#8220;undo&#8221; adding 6 by subtracting 6, and to keep the equality we must subtract 6 from both sides. Use the Subtraction Property of Equality.<\/td>\n<td><span id=\"eip-id1168468595447\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168469636495\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Now all the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>s are on the left and the constant on the right.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Division Property of Equality.<\/td>\n<td><span id=\"eip-id1168468510734\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467161449\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168469706628\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469888129\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469781731\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466173400\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_039_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492881928\" data-type=\"problem\">\n<p id=\"fs-id1731988\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-523d3bec1c91d11f19149d13226900d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#52;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1457111\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166493265803\"><em data-effect=\"italics\">x<\/em> = \u22124<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497370080\" data-type=\"problem\">\n<p id=\"fs-id1912137\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f290a3886e1926b8490711272e83b891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;&#43;&#51;&#61;&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166488289045\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166498100876\"><em data-effect=\"italics\">a<\/em> = \u22128<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166498437180\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c0ff7fc24e106f8adc3a165f595c2f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#45;&#55;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166491426141\" data-type=\"solution\">\n<p id=\"fs-id1895587\">Notice that the variable is only on the left side of the equation, so this will be the variable side and the right side will be the constant side. Since the left side is the variable side, the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> is out of place. It is subtracted from the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85ca23a1e42ccdfafecd1cf9622b44c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/>, so to \u2018undo\u2019 subtraction, add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> to both sides.<\/p>\n<table id=\"eip-id1168469592645\" style=\"width: 100%;\" summary=\"The first line says 2y minus 7 equals 15. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says \u201cAdd 7 to both sides\u201d and shows 2y minus 7 plus a red 7 equals 15 plus a red 7. The next line says \u201cSimplify\u201d and shows 2y equals 22. Below it says \u201cThe variables are now on one side and the constants on the other.\u201d The next line says \u201cDivide both sides by 2\u201d and shows 2y over a red 2 equals 22 over a red 2. The next line says \u201cSimplify\u201d and shows y equals 11. The next line says \u201cCheck\u201d and shows 2y minus 7 equals 15. Below is \u201cSubstitute y equals 11\u201d and shows 2 times a red 11 minus 7, equal sign with a question mark, 15. Below is 22 minus 7, equal sign with a question mark, 15. The last line says 15 equals 15, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468593491\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add 7 to both sides.<\/td>\n<td><span id=\"eip-id1168468264489\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467251501\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">The variables are now on one side and the constants on the other.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1168468309146\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168468455363\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468406041\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c0f05c9c8eee23a55f79fb8abde9cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"50\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><span id=\"eip-id1168467196582\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468627978\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467473346\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_023_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492075765\" data-type=\"problem\">\n<p id=\"fs-id1166492068788\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9195f5bce49a2a4822f976f505c26faf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#57;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1431377\"><em data-effect=\"italics\">y<\/em> = 5<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1304456\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7da847b5f4324bdc1926d993507432e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#109;&#45;&#56;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"97\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1324771\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">m<\/em> = 9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1515036\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve an Equation with Variables on Both Sides<\/h1>\n<p id=\"fs-id1390876\">What if there are variables on both sides of the equation? We will start like we did above\u2014choosing a <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> side and a constant side, and then use the Subtraction and Addition Properties of Equality to collect all variables on one side and all <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> on the other side. Remember, what you do to the left side of the equation, you must do to the right side too.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1302551\" data-type=\"problem\">\n<p id=\"fs-id1166491232107\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32deb1b558a621ed396537e4647157f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#61;&#52;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"92\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1858532\" data-type=\"solution\">\n<div data-type=\"title\">Solution<\/div>\n<p id=\"fs-id1832872\">Here the variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, is on both sides, but the constants appear only on the right side, so let\u2019s make the right side the \u201cconstant\u201d side. Then the left side will be the \u201cvariable\u201d side.<\/p>\n<table id=\"eip-id1168465095460\" style=\"width: 100%;\" summary=\"The first line says 5x equals 4x plus 7. The left side is labeled \u201cvariable\u201d in red and the right side is labeled \u201cconstant\u201d in red. The next line says \u201cWe don't want any variables on the right, so subtract the 4x from both sides.\u201d Beside that is 5x minus a red 4x equals 4x minus a red 4x plus 7. The next line says \u201cSimplify\u201d and shows x equals 7. Below is \u201cWe have all the variables on one side and the constants on the other. We have solved the equation.\u201d The next line says \u201cCheck\u201d and shows 5x equals 4x plus 7. Below is \u201cSubstitute 7 for x\u201d and 5 times a red 7 equals 4 times a red 7 plus 7. Below that is 35 equals 28 plus 7, then 35 equals 35.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468630242\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We don&#8217;t want any variables on the right, so subtract the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fa4d35b5c4377934245a54e07e43e7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468653139\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467114351\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We have all the variables on one side and the constants on the other. We have solved the equation.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468467076\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute 7 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468229247\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468264497\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468711064\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_024_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1470170\" data-type=\"problem\">\n<p id=\"fs-id1445738\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddbb4280bd1c8bf27a6b4c9d6a6ca1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#110;&#61;&#53;&#110;&#43;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"102\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">n<\/em> = 10<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1436190\" data-type=\"problem\">\n<p id=\"fs-id1166493760719\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf5a51491d572ace13de4a8a8e62b8e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#99;&#61;&#45;&#55;&#99;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"113\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166498435818\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1297432\"><em data-effect=\"italics\">c<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497309664\" data-type=\"problem\">\n<p id=\"fs-id1403520\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b557bd9139acb85ea3171917e885dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#56;&#61;&#55;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1355584\" data-type=\"solution\">\n<p>The only constant, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>, is on the left side of the equation and variable, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>, is on both sides. Let\u2019s leave the constant on the left and collect the variables to the right.<\/p>\n<table id=\"eip-id1168468768462\" style=\"width: 100%;\" summary=\"The first line says 5y minus 8 equals 7y. The left side is labeled \u201cconstant\u201d in red and the right side is labeled \u201cvariable\u201d in red. The next line says \u201cSubtract 5y from both sides\u201d and shows 5y minus a red 5y minus 8 equals 7y minus a red 5y. The next line says \u201cSimplify\u201d and shows negative 8 equals 2y. The next line says \u201cWe have the variables on the right and the constants on the left. Divide both sides by 2.\u201d Beside that is negative 8 over a red 2 equals 2y over a red 2. The next line says \u201cSimplify\u201d and shows negative 4 equals y. The next line says \u201cRewrite with the variable on the left\u201d and shows y equals negative 4. The last step says \u201cCheck. Let y equal negative 4.\u201d Beside that is 5y minus 8 equals 7y, then 5 times a red negative 4 minus 8 equals 7 times a red negative 4, then negative 20 minus 8 equals negative 28, then negative 28 equals negative 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468713810\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ced6e13bb9f8c850f4b8c91f46ef4889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168467116420\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467187881\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have the variables on the right and the constants on the left. Divide both sides by 2.<\/td>\n<td><span id=\"eip-id1168467251083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467129401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the variable on the left.<\/td>\n<td><span id=\"eip-id1168468394421\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468727587\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168467314260\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468411184\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468411200\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_025_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166483685326\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7823d9c74bc81de5846bca5ffc50ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#112;&#45;&#49;&#52;&#61;&#53;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1691348\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1470064\"><em data-effect=\"italics\">p<\/em> = \u22127<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497310585\" data-type=\"problem\">\n<p id=\"fs-id1166494705142\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b213fdbef05b5d0f24154b93ac79f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#109;&#43;&#57;&#61;&#53;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491402673\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1559521\"><em data-effect=\"italics\">m<\/em> = \u22123<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166482688772\" data-type=\"exercise\">\n<div id=\"fs-id1166483685326\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166489093428\" data-type=\"problem\">\n<p id=\"fs-id1558937\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39983a4d2f9e2253cd89b3efada635e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#61;&#45;&#120;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"106\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492723804\" data-type=\"solution\">\n<p id=\"fs-id1166498045277\">The only constant, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/>, is on the right, so let the left side be the variable side.<\/p>\n<table id=\"eip-id1168467377760\" style=\"width: 100%;\" summary=\"The first line says 7x equals negative x plus 24. The left side is labeled \u201cvariable side\u201d in red and the right side is labeled \u201cconstant side\u201d in red. The next line says \u201cRemove the negative x from the right side by adding x to both sides.\u201d Beside that is 7x plus a red x equals negative x plus a red x plus 24. The next line says \u201csimplify\u201d and shows 8x equals 24. The following line says \u201cAll the variables are on the left and the constants are on the right. Divide both sides by 8.\u201d Beside that is 8x over a red 8 equals 24 over a red 8. The next line says \u201csimplify\u201d and shows x equals 3. The next line says \u201ccheck\u201d and shows 7x equals negative x plus 24. Below that is \u201cSubstitute x equals 3\u201d and shows 7 times a red 3, equal sign with a question mark, negative red 3 plus 24. The last line says 21 equals 21.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467238229\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Remove the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/> from the right side by adding <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> to both sides.<\/td>\n<td><span id=\"eip-id1168467263067\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467359022\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>All the variables are on the left and the constants are on the right. Divide both sides by 8.<\/td>\n<td><span id=\"eip-id1168468713840\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467311311\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168465131873\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_026_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494586231\" data-type=\"problem\">\n<p id=\"fs-id1948298\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93e094b09965f176d7031f4322ceb48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#106;&#61;&#45;&#52;&#106;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1524724\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490806219\"><em data-effect=\"italics\">j<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482688714\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9956244e9e31691e211d04b40581e380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#104;&#61;&#45;&#52;&#104;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"114\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id590470\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1355386\"><em data-effect=\"italics\">h<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations with Variables and Constants on Both Sides<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1244059\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1767277\">The next example will be the first to have variables <em data-effect=\"italics\">and<\/em> constants on both sides of the equation. As we did before, we\u2019ll collect the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> terms to one side and the <span class=\"no-emphasis\" data-type=\"term\">constants<\/span> to the other side.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497196207\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e29c99be37d7999da42bd5fdef732e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#53;&#61;&#54;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166484059766\" data-type=\"solution\">\n<p>Start by choosing which side will be the variable side and which side will be the constant side. The variable terms are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21c22354b95d8047439895fca18899e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9dbdb28b1297d32a21861bc74971aeae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, make the left side the variable side and so the right side will be the constant side.<\/p>\n<table id=\"eip-id1168468709344\" style=\"width: 100%;\" summary=\"The first line says 7x plus 5 equals 6x plus 2. The next line says \u201cCollect the variable terms to the left side by subtracting 6x from both sides.\u201d Beside that is 7x minus a red 6x plus 5 equals 6x minus a red 6x plus 2. The next line says \u201cCombine like terms\u201d and shows x plus 5 equals 2. The next line says \u201cNow, collect the constants to the right side by subtracting 5 from both sides.\u201d Beside that is x plus 5 minus a red 5 equals 2 minus a red 5. The next line says \u201cSimplify\u201d and shows x equals negative 3. The next line says \u201cThe solution is x equals negative 3.\u201d The last step says \u201cCheck: Let x equal negative 3.\u201d Beside that is 7x plus 5 equals 6x plus 2. The next line says 7 times a red negative 3 plus 5, equal sign with a question mark, 6 times a red negative 3 plus 2. Below that is negative 21 plus 5, equal sign with a question mark, negative 18 plus 2. The last line says negative 16 equals negative 16.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468537221\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the variable terms to the left side by subtracting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9dbdb28b1297d32a21861bc74971aeae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168467429656\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467338898\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Now, collect the constants to the right side by subtracting 5 from both sides.<\/td>\n<td><span id=\"eip-id1168467330763\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467330780\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\"><span id=\"eip-id1168468571132\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_027_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1397980\" data-type=\"problem\">\n<p id=\"fs-id1359684\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43882bcb4556692cbb2bf4173364f58e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#43;&#56;&#61;&#54;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"130\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">x<\/em> = \u22121<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1357188\" data-type=\"problem\">\n<p id=\"fs-id1692853\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bc8c35b7a36f236da45288e6350efba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#43;&#52;&#61;&#55;&#121;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1469991\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1249270\"><em data-effect=\"italics\">y<\/em> = 4<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1763313\">We\u2019ll summarize the steps we took so you can easily refer to them.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Solve an Equation with Variables and Constants on Both Sides<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168468371331\" class=\"stepwise\" type=\"1\">\n<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\n<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>, using the Multiplication or Division Property of Equality.<\/li>\n<li>Check the solution by substituting it into the original equation.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1166484081154\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<p>It is a good idea to make the variable side the one in which the variable has the larger coefficient. This usually makes the arithmetic easier.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1486587\" data-type=\"problem\">\n<p id=\"fs-id1332952\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-378b19ec46b4e88efc4d007882237a65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#110;&#45;&#50;&#61;&#45;&#51;&#110;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"138\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166482443035\" data-type=\"solution\">\n<p id=\"fs-id1166493771208\">We have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61e315c335716d1c60fffd82ccb82e52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: 0px;\" \/> on the left and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b7f3f3997ff61f90da5856bae2ddcf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"33\" style=\"vertical-align: 0px;\" \/> on the right. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>, make the left side the \u201cvariable\u201d side.<\/p>\n<table id=\"eip-id1168467335489\" style=\"width: 100%;\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \u201cWe don't want variables on the right side - add 3n to both sides to leave only constants on the right. Beside that is 6n plus a red 3n minus 2 equals negative 3n plus a red 3n plus 7. The next line says \u201cCombine like terms\u201d and shows 9n minus 2 equals 7. The next line says \u201cWe don't want any constants on the left side, so add 2 to both sides.\u201d Beside that is 9n minus 2 plus a red 2 equals 7 plus a red 2. The next line says \u201cSimplify\u201d and shows 9n equals 9. The next line says \u201cThe variable term is on the left and the constant term is on the right. To get the coefficient of n to be one, divide both sides by 9. Beside that is 9n over a red 9 equals 9 over a red 9. The next line says \u201cSimplify\u201d and shows n equals 1. The next line says \u201cCheck\u201d and shows 6n minus 2 equals negative 3n plus 7. Below that is \u201cSubstitute 1 for n\u201d and 6 times a red 1 minus 2 followed by an equal sign with a question mark, then negative 3 times a red 1 plus 7. The last line says 4 equals 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469614901\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We don&#8217;t want variables on the right side\u2014add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0bd6fa46a14c151a72b15ba27270c306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: 0px;\" \/> to both sides to leave only constants on the right.<\/td>\n<td><span id=\"eip-id1168469574727\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168466072161\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We don&#8217;t want any constants on the left side, so add 2 to both sides.<\/td>\n<td><span id=\"eip-id1168469616858\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469468579\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The variable term is on the left and the constant term is on the right.<br \/>\nTo get the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> to be one, divide both sides by 9.<\/td>\n<td><span id=\"eip-id1168469617677\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469613794\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute 1 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469485471\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_028_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482410079\" data-type=\"problem\">\n<p id=\"fs-id1481548\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53858c0161fc49d557a8dd40f351bc82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#113;&#45;&#53;&#61;&#45;&#52;&#113;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"133\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1945999\"><em data-effect=\"italics\">q<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166492887225\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1565ba8385933dba31947071373cdd7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#110;&#45;&#51;&#61;&#110;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"115\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166493762183\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1741775\"><em data-effect=\"italics\">n<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166495279643\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1953082\" data-type=\"exercise\">\n<div id=\"fs-id1166482410079\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1857913\" data-type=\"problem\">\n<p id=\"fs-id1445284\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e35a6347caa7c271c4dedef727661ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#45;&#55;&#61;&#53;&#97;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"121\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492881878\" data-type=\"solution\">\n<p>This equation has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02baaffe4ddb6a44400eb7ba175e566c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> on the left and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9360ef9fb862d7bf0e669eb7b4606fea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> on the right. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>, make the right side the variable side and the left side the constant side.<\/p>\n<table id=\"eip-id1168466004451\" style=\"width: 100%;\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \u201cWe don't want variables on the right side - add 3n to both sides to leave only constants on the right. Beside that is 6n plus a red 3n minus 2 equals negative 3n plus a red 3n plus 7. The next line says \u201cCombine like terms\u201d and shows 9n minus 2 equals 7. The next line says \u201cWe don't want any constants on the left side, so add 2 to both sides.\u201d Beside that is 9n minus 2 plus a red 2 equals 7 plus a red 2. The next line says \u201cSimplify\u201d and shows 9n equals 9. The next line says \u201cThe variable term is on the left and the constant term is on the right. To get the coefficient of n to be one, divide both sides by 9. Beside that is 9n over a red 9 equals 9 over a red 9. The next line says \u201cSimplify\u201d and shows n equals 1. The next line says \u201cCheck\u201d and shows 6n minus 2 equals negative 3n plus 7. Below that is \u201cSubstitute 1 for n\u201d and 6 times a red 1 minus 2 followed by an equal sign with a question mark, then negative 3 times a red 1 plus 7. The last line says 4 equals 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469497825\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02baaffe4ddb6a44400eb7ba175e566c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> from both sides to remove the variable term from the left.<\/td>\n<td><span id=\"eip-id1168469353933\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469353950\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 8 from both sides to remove the constant from the right.<\/td>\n<td><span id=\"eip-id1168469805558\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466269006\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 3 to make 1 the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466048053\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466113284\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0a1ebc3825fb7a3acd97d2c5ebf8b41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469686306\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_029_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1458532\">Note that we could have made the left side the variable side instead of the right side, but it would have led to a negative coefficient on the variable term. While we could work with the negative, there is less chance of error when working with positives. The strategy outlined above helps avoid the negatives!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497443661\" data-type=\"problem\">\n<p id=\"fs-id1498474\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40288073cd7cedc357e9efa96a89a2cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#45;&#50;&#61;&#54;&#97;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"130\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1573469\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">a<\/em> = \u22125<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1476865\" data-type=\"problem\">\n<p id=\"fs-id1547301\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83d5669fd6c032c78fc2ce2d575f1c2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&#45;&#49;&#61;&#55;&#107;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1956097\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490837958\"><em data-effect=\"italics\">k<\/em> = \u22126<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>To solve an equation with fractions, we still follow the same steps to get the solution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491053390\" data-type=\"problem\">\n<p id=\"fs-id1166490838129\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1411c037c34fc39221768e45d138ffc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#53;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1742076\" data-type=\"solution\">\n<p id=\"fs-id1166491054296\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eadb3de75c7c00057d0aede78f9ebd79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8fa03e1b526c6d07ec843385490ca4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>, make the left side the variable side and the right side the constant side.<\/p>\n<table id=\"eip-id1168469779179\" style=\"width: 100%;\" summary=\"The first line says three-halves x plus 5 equals one-half x minus 3. The next line says, \u201cSubtract one-half x from both sides,\u201d and shows three-halves x minus a red one-half x plus 5 equals one-half x minus a red one-half x minus 3. The next line says, \u201cCombine like terms,\u201d and shows x plus 5 equals negative 3. The next line says, \u201cSubtract 5 from both sides,\u201d and shows x plus 5 minus a red 5 equals negative 3 minus a red 5. The next line says, \u201cSimplify,\u201d and shows x equals negative 8. The last step says, \u201cCheck: Let x equal negative 8.\u201d Beside that is three-halves x plus 5 equals one-half x minus 3. Below that is three-halves times a red negative 8 plus 5 equals one-half times a red negative 8 minus 3. The next line shows negative 12 plus 5 equals negative 4 minus 3. The last line shows negative 7 equals negative 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467544617\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b61981392063277276609ee2214ce59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"19\" style=\"vertical-align: -6px;\" \/> from both sides.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168468496654\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467366826\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168467366844\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168468743331\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7852d0704798164bd2ce5b572ac50cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468350715\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_030_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493276476\" data-type=\"problem\">\n<p id=\"fs-id1166497276823\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d22a9c122e2d44ecb1820c9baeecebfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#49;&#50;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166494721481\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497294974\"><em data-effect=\"italics\">x<\/em> = 10<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491270654\" data-type=\"problem\">\n<p id=\"fs-id1166497354048\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d7e841901d2c69cbcaa2027c942c931_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#49;&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"135\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1436738\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491248892\"><em data-effect=\"italics\">y<\/em> = \u22123<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166498082088\">We follow the same steps when the equation has decimals, too.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490863127\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8147ca0d1fcb9e15db3af45c1786b91a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#52;&#120;&#43;&#52;&#61;&#49;&#46;&#54;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"149\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1517936\" data-type=\"solution\">\n<p id=\"fs-id1166490904889\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1605f75320ddc984a1418c7acf8d1a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5cd5cd6c2fb3862949d66708486dcfd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/>, make the left side the variable side and the right side the constant side.<\/p>\n<table id=\"eip-id1168466001051\" style=\"width: 100%;\" summary=\"The top line says 3.4x plus 4 equals 1.6x minus 5. The next line says, \u201cSubtract 1.6x from both sides,\u201d and shows 3.4x minus a red 1.6x plus 4 equals 1.6x minus a red 1.6x minus 5. The next line says, \u201cCombine like terms,\u201d and shows 1.8x plus 4 equals negative 5. The next line says, \u201cSubtract 4 from both sides,\u201d and shows 1.8x plus 4 minus a red 4 equals negative 5 minus a red 4. The next line says, \u201cSimplify,\u201d and shows 1.8x equals negative 9. The next line says, \u201cUse the division property of equality,\u201d and shows 1.8x over a red 1.8 equals negative 9 over a red 1.8. The next line says, \u201cSimplify,\u201d and shows x equals negative 5. The last step says, \u201cCheck: Substitute x equals negative 5.\u201d Beside that is 3.4x plus 4 equals 1.6x minus 5. Below that is 3.4 times a red negative 5 plus 4 equals 1.6 times a red negative 5 minus 5. Below that is negative 17 plus 4 equals negative 8 minus 5. The last line shows negative 13 equals negative 13.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469879099\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d26fe8cb7671ae24e293c9aafe78c311_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168466657795\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168466657811\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 4 from both sides.<\/td>\n<td><span id=\"eip-id1168469616764\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469617706\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Division Property of Equality.<\/td>\n<td><span id=\"eip-id1168469692083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469747571\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469461335\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_031_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490838002\" data-type=\"problem\">\n<p id=\"fs-id1166493760978\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cddc80f767e08012ec6b671fa3215573_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#56;&#120;&#43;&#49;&#50;&#61;&#45;&#49;&#46;&#52;&#120;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"173\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1329708\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166479093904\"><em data-effect=\"italics\">x<\/em> = \u22125<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497359897\" data-type=\"problem\">\n<p id=\"fs-id1945758\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-990319523a11fdb7c2c8763ddf1c44cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#54;&#121;&#43;&#56;&#61;&#49;&#46;&#50;&#121;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"149\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166479038932\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1833479\"><em data-effect=\"italics\">y<\/em> = \u22125<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations Using a General Strategy<\/h1>\n<\/div>\n<div id=\"fs-id1166492018062\" class=\"bc-section section\" data-depth=\"1\">\n<p>Each of the first few sections of this chapter has dealt with solving one specific form of a <span class=\"no-emphasis\" data-type=\"term\">linear equation<\/span>. It\u2019s time now to lay out an overall strategy that can be used to solve <em data-effect=\"italics\">any<\/em> linear equation. We call this the <em data-effect=\"italics\">general strategy<\/em>. Some equations won\u2019t require all the steps to solve, but many will. Simplifying each side of the equation as much as possible first makes the rest of the steps easier.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Use a General Strategy for Solving Linear Equations<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168467248588\" class=\"stepwise\" type=\"1\">\n<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\n<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable term to equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>. Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\n<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1445020\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1510057\" data-type=\"problem\">\n<p id=\"fs-id1392091\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2327bc22604334625835f9e5cf154299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168468387403\" style=\"width: 100%;\" summary=\"Simplify each side of the equation as much as possible. Use the Distributive Property.\u201d Beside that is 3 times parentheses x plus 2 equals 18. The next line says, \u201cCollect all variable terms on one side of the equation - all xs are already on the left side.\u201d Beside that is 3x plus 6 equals 18. The next line says, \u201cCollect constant terms on the other side of the equation. Subtract 6 from each side.\u201d Beside that is 3x plus 6 minus a red 6 equals 18 minus a red 6. The next line says, \u201cSimplify,\u201d and shows 3x equals 12. The next line says, \u201cMake the coefficient of the variable term to equal 1. Divide each side by 3.\u201d Beside that is 3x over a red 3 equals 12 over a red 3. The next line says, \u201cSimplify,\u201d and shows x equals 4. The last step says, \u201cCheck the solution. Let x equal 4.\u201d Below that is 3 times parentheses x plus 2 equals 18. Below that is 3 times parentheses red 4 plus 2, equal sign with a question mark, 18. Below that is 3 times 6, equal sign with a question mark, 18. The last line shows 18 equals 18 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1187288\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side of the equation as much as possible.<br \/>\nUse the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468533951\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect all variable terms on one side of the equation\u2014all <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>s are already on the left side.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Collect constant terms on the other side of the equation.<br \/>\nSubtract 6 from each side<\/td>\n<td><span id=\"eip-id1168467248487\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468721440\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Make the coefficient of the variable term equal to 1. Divide each side by 3.<\/td>\n<td><span id=\"eip-id1168468646687\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468646704\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168465131755\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_032_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1735280\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e006e4f8396be2de905a7126b7b5b651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1202244\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">x<\/em> = 4<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1367765\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec26a9edf119dc75acf6c6b0805e18f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166484109032\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1431126\"><em data-effect=\"italics\">y<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1258354\" data-type=\"problem\">\n<p id=\"fs-id1285644\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02a0efd6fb1a352f359d4c0debb2149b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469659755\" style=\"width: 100%; height: 363px;\" summary=\"Simplify each side of the equation as much as possible by distributing. The only x term is on the left side, so all variable terms are on the left side of the equation.\u201d Beside that is negative x minus 5 equals 7. The next line says, \u201cAdd 5 to both sides to get all constant terms on the right side of the equation.\u201d Beside that is negative x minus 5 plus a red 5 equals 7 plus a red 5. The next line says, \u201cSimplify,\u201d and shows negative x equals 12. The next line says, \u201cMake the coefficient of the variable term equal to 1 by multiplying both sides by negative 1.\u201d Beside that is a red negative 1 times negative x equals a red negative 1 times 12. The next line says, \u201cSimplify,\u201d and shows x equals negative 12. The last step says, \u201cCheck: Let x equal negative 12.\u201d Beside that is negative parentheses x plus 5 equals 7, then negative parentheses red negative 12 plus 5 equals 7, then negative negative 7 equals 7, then 7 equals 7.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\"><\/td>\n<td style=\"height: 24px;\"><span id=\"eip-id1168466183184\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px;\">Simplify each side of the equation as much as possible by distributing.<br \/>\nThe only <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> term is on the left side, so all variable terms are on the left side of the equation.<\/td>\n<td style=\"height: 33px;\"><span id=\"eip-id1168466110663\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Add 5 to both sides to get all constant terms on the right side of the equation.<\/td>\n<td style=\"height: 28px;\"><span id=\"eip-id1168469735440\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Simplify.<\/td>\n<td style=\"height: 28px;\"><span id=\"eip-id1168466091761\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px;\">Make the coefficient of the variable term equal to 1 by multiplying both sides by -1.<\/td>\n<td style=\"height: 26px;\"><span id=\"eip-id1168466322456\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px;\">Simplify.<\/td>\n<td style=\"height: 24px;\"><span id=\"eip-id1168469798411\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 134px;\">\n<td style=\"height: 134px;\">Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e03ecf0c8d4b79d9b63545f9baa1d3f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"65\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"height: 134px;\"><span id=\"eip-id1168048774145\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168048774155\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168048774165\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168048774174\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_033_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1685205\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1479602\" data-type=\"exercise\">\n<div id=\"fs-id1166484109032\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492696720\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd2573e062e8f587d34a2f69d8c5dfc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1729772\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166479011445\"><em data-effect=\"italics\">y<\/em> = \u22126<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166494736971\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e28e24d04b07bcbb67c1bdd0f5c663a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1731591\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166494721814\"><em data-effect=\"italics\">z<\/em> = 8<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166491410544\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1166492696720\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1771048\" data-type=\"problem\">\n<p id=\"fs-id1166484125384\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d188035e5682f1f72584b4876f2573c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469612809\" style=\"width: 100%;\" summary=\"The top line shows 4 times parentheses x minus 2 plus 5 equals negative 3. The next line says, \u201cSimplify each side of the equation as much as possible. Distribute.\u201d Beside that is 4x minus 8 plus 5 equals negative 3. The next line says, \u201cCombine like terms,\u201d and shows 4x minus 3 equals negative 3. The next line says, \u201cThe only x is on the left side, so all variable terms are on one side of the equation. Add 3 to both sides to get all constant terms on the other side of the equation.\u201d Beside that is 4x minus 3 plus a red 3 equals negative 3 plus a red 3. The next line says, \u201cSimplify,\u201d and shows 4x equals 0. The next line says, \u201cMake the coefficient of the variable term to equal to 1 by dividing both sides by 4.\u201d Beside that is 4x over a red 4 equals 0 over a red 4. The next line says, \u201cSimplify,\u201d and shows x equals 0. The last step says, \u201cCheck: Let x equal 0.\u201d Beside that is 4 times parentheses x minus 2 plus 5 equals negative 3. The next line says 4 times parentheses red 0 minus 2 plus 5 equals negative 3. Below that is 4 times negative 2 plus 5 equals negative 3, then negative 8 plus 5 equals negative 3, then negative 3 equals negative 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469614509\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side of the equation as much as possible.<br \/>\nDistribute.<\/td>\n<td><span id=\"eip-id1168466081811\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms<\/td>\n<td><span id=\"eip-id1168466174407\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The only <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is on the left side, so all variable terms are on one side of the equation.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add 3 to both sides to get all constant terms on the other side of the equation.<\/td>\n<td><span id=\"eip-id1168466034680\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469615730\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Make the coefficient of the variable term equal to 1 by dividing both sides by 4.<\/td>\n<td><span id=\"eip-id1168465988158\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469839767\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469773952\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_034_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1869700\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b2c4f95cb540be770644b4723118540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166493760882\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166493485396\"><em data-effect=\"italics\">a<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1417482\" data-type=\"problem\">\n<p id=\"fs-id1166488299701\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d52a466ca54488260c24f130392923f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166482135584\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1538857\"><em data-effect=\"italics\">n<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1502246\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b9f8a8e5285d83146663c13b4507f65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p>Be careful when distributing the negative.<\/p>\n<table id=\"eip-id1168467174932\" style=\"width: 100%;\" summary=\"The top line says 8 minus 2 parentheses 3y plus 5 equals 0. The next line says, \u201cSimplify - use the Distributive Property,\u201d and shows 8 minus 6y minus 10 equals 0. The next line says, \u201cCombine like terms,\u201d and shows negative 6y minus 2 equals 0. The next line says, \u201cAdd 2 to both sides to collect constants on the right,\u201d and shows negative 6y minus 2 plus a red 2 equals 0 plus a red 2. The next line says, \u201cSimplify,\u201d and shows negative 6y equals 2. The next line says, \u201cDivide both sides by negative 6,\u201d and shows negative 6y over a red negative 6 equals 2 over a red negative 6. The following line says, \u201cSimplify,\u201d and shows y equals negative one-third. The last step says, \u201cCheck: let y equal negative one-third.\u201d Beside that is the original equation. Below that is 8 minus 2 parentheses 3 times a red negative one-third plus 5 equals 0. Below is 8 minus 2 parentheses negative 1 plus 5 equals 0, then 8 minus 2 times 4 equals 0, then 8 minus 8 equals 0, and then 0 equals 0.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467359014\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014use the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468376858\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168468567044\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 2 to both sides to collect constants on the right.<\/td>\n<td><span id=\"eip-id1168468567060\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467473445\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by \u22126.<\/td>\n<td><span id=\"eip-id1168467148757\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467148774\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c6dfce7ea311b94f51717efc951c245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><span id=\"eip-id1168467174781\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_035_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1482353\" data-type=\"problem\">\n<p id=\"fs-id1166494737529\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cb921bacc174b647f1aabb3a2c54d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#106;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4874eebd278f01816931e53b52b1804a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#106;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1361205\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2bc5d875061c3d1e2e6701637e9a945f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"165\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1271847\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1732922\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9339b82b1ffffbe08086d2a1216e45e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1476001\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0a99db979838405e3f796ee5cff9997_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#61;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"225\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1218520\" data-type=\"solution\">\n<table id=\"eip-id1168468704060\" style=\"width: 100%;\" summary=\"The top line says 3 parentheses x minus 2 minus 5 equals 4 parentheses 2x plus 1 plus 5. The next line says, \u201cDistribute,\u201d and shows 3x minus 6 minus 5 equals 8x plus 4 plus 5. The next line says, \u201cCombine like terms,\u201d and shows 3x minus 11 equals 8x plus 9. The next line says \u201cSubtract 3x to get all the variables on the right since 8 is greater than 3,\u201d and shows 3x minus a red 3x minus 11 equals 8x minus a red 3x plus 9. The next line says, \u201cSimplify,\u201d and shows negative 11 equals 5x plus 9. The next line says, \u201cSubtract 9 to get the constants on the left,\u201d and shows negative 11 minus a red 9 equals 5x plus 9 minus a red 9. The net line says, \u201cSimplify,\u201d and shows negative 20 equals 5x. The next line says, \u201cDivide by 5,\u201d and shows negative 20 over a red 5 equals 5x over a red 5. The next line says, \u201cSimplify,\u201d and shows negative 4 equals x. The last step says, \u201cCheck. Substitute x equals negative 4.\u201d Beside this is the original equation, followed by 3 times parentheses red negative 4 minus 2 minus 5 equals 4 times parentheses 2 times negative 4 plus 1 plus 5. Below that is 3 times negative 6 minus 5 equals 4 times parentheses negative 8 plus 1 plus 5. Below that is negative 18 minus 5 equals 4 times negative 7 plus 5. Below that is negative 23 equals negative 28 plus 5. The last line shows negative 23 equals negative 23.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466230669\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469522784\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168465986112\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> to get all the variables on the right since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466281124\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469801111\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 9 to get the constants on the left.<\/td>\n<td><span id=\"eip-id1168466036190\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466215053\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 5.<\/td>\n<td><span id=\"eip-id1168466267864\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466026625\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-304ea2efde2d40e50b36f8ebe80f0017_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#61;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466463596\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_036_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1453989\" data-type=\"problem\">\n<p id=\"fs-id1341235\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-393ba0f2bd3ed3449fbc5f008dfd8116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#112;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"232\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490921468\"><em data-effect=\"italics\">p<\/em> = \u22122<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166484083199\" data-type=\"problem\">\n<p id=\"fs-id1948566\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da7f3442d4e666cfcc2b07af22757d8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#113;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"222\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1324992\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1869648\"><em data-effect=\"italics\">q<\/em> = \u22128<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492690992\" data-type=\"problem\">\n<p id=\"fs-id1482586\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cfbc1a2001102500af12e0865948d05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"139\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168469851853\" style=\"width: 100%;\" summary=\"The top line says one-half times parentheses 6x minus 2 equals 5 minus x. The next line says, \u201cDistribute,\u201d and shows 3x minus 1 equals 5 minus x. The next line says, \u201cAdd x to get all the variables on the left,\u201d and shows 3x minus 1 plus a red x equals 5 minus x plus a red x. The next line says, \u201cSimplify,\u201d and shows 4x minus 1 equals 5. The next line says, \u201cAdd 1 to get constants on the right,\u201d and shows 4x minus 1 plus a red 1 equals 5 plus a red 1. The next line says, \u201cSimplify,\u201d and shows 4x equals 6. The next line says, \u201cDivide by 4,\u201d and shows 4x over a red 4 equals 6 over a red 4. The next line says, \u201cSimplify,\u201d and shows x equals three-halves. The last step says, \u201cCheck: Let x equal three-halves.\u201d Beside that is the original equation followed by one-half times parentheses 6 times a red three-halves minus 2 equals 5 minus a red three-halves. Below that is one-half times parentheses 9 minus 2 equals ten-halves minus three-halves, then one-half times 7 equals 7 halves, then 7 halves equals 7 halves.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466324380\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168465998394\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> to get all the variables on the left.<\/td>\n<td><span id=\"eip-id1168466204103\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466661049\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 1 to get constants on the right.<\/td>\n<td><span id=\"eip-id1168469456166\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469577022\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 4.<\/td>\n<td><span id=\"eip-id1168466121572\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466166059\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82aa8812cbd6ad536dcb3c4fddfef6d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466426974\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_037_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493761572\" data-type=\"problem\">\n<p id=\"fs-id1166493721820\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a583371704d17603b9eece946a1239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#117;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#45;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"139\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166492013626\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1704714\"><em data-effect=\"italics\">u<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1361128\" data-type=\"problem\">\n<p id=\"fs-id1166491409253\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e00847127c6a5e0c4694dfbf9b38985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#120;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#43;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166497359267\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490773708\"><em data-effect=\"italics\">x<\/em> = 4<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>In many applications, we will have to solve equations with decimals. The same general strategy will work for these equations.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491403013\" data-type=\"problem\">\n<p id=\"fs-id1486914\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-611822431b7494c3cfa44505a8fa82e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#48;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#120;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"245\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1449046\" data-type=\"solution\">\n<table id=\"eip-id1168468569426\" style=\"width: 100%;\" summary=\"The top line says 0.24 times parentheses 100x plus 5 equals 0.4 times parentheses 30x plus 15. The next line says, \u201cDistribute,\u201d and shows 24x plus 1.2 equals 12x plus 6. The next line says, \u201cSubtract 12x to get the xs to the left,\u201d and shows 24x plus 1.2 minus a red 12x equals 12x plus 6 minus a red 12x. The next line says, \u201cSimplify,\u201d and shows 12x plus 1.2 equals 6. The next line says, \u201cSubtract 1.2 to get the constants to the right,\u201d and shows 12x plus 1.2 minus a red 1.2 equals 6 minus a red 1.2. The next line says, \u201cSimplify,\u201d and shows 12x equals 4.8. The next line says, \u201cDivide,\u201d and shows 12x over a red 12 equals 4.8 over a red 12. The next line says, \u201cSimplify,\u201d and shows x equals 0.4. The next line says, \u201cCheck,\u201d and shows the original equation. Below that, it says, \u201cLet x equal 0.4,\u201d and shows 0.24 times parentheses 100 times a red 0.4 plus 5, equal sign with a question mark, 0.4 times parentheses 30 times a red 0.4 plus 15. Below that is 0.24 times parentheses 40 plus 5, equal sign with a question mark, 0.4 times parentheses 12 plus 15. Below that is 0.24 times 45, equal sign with a question mark, 0.4 times 27. The last line says 10.8 equals 10.8 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469856402\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469683989\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cc37a51efcd4650021f5d9d8222e893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> to get all the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>s to the left.<\/td>\n<td><span id=\"eip-id1168466144870\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469868305\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 1.2 to get the constants to the right.<\/td>\n<td><span id=\"eip-id1168469491155\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469594198\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1168469544803\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469829057\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c3dec8032bdf667e9b1d8cd5191746c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466203358\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_03_038_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497435575\" data-type=\"problem\">\n<p id=\"fs-id1296459\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66173cad7c9c268d72e17dcd75e9e1a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#48;&#110;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#53;&#110;&#43;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"246\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1789082\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166488297923\">1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1542714\" data-type=\"problem\">\n<p id=\"fs-id1166491412269\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8731a5d569fdd04fe3a3c5353db2781e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#48;&#109;&#45;&#49;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#48;&#109;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"265\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1460794\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166494770264\">\u22121<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"eip-578\">\n<li><strong>Solve an equation with variables and constants on both sides<\/strong>\n<ol id=\"eip-id1170322988380\" class=\"stepwise\" type=\"1\">\n<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\n<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable 1, using the Multiplication or Division Property of Equality.<\/li>\n<li>Check the solution by substituting into the original equation.<\/li>\n<\/ol>\n<\/li>\n<li><strong>General strategy for solving linear equations<\/strong>\n<ol id=\"eip-id1170324010914\" class=\"stepwise\" type=\"1\">\n<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\n<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable term to equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\n<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<div id=\"fs-id1166490790567\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1681739\" data-type=\"exercise\">\n<h1 id=\"fs-id1166497435575\" data-type=\"problem\">Practice Makes Perfect<\/h1>\n<div id=\"fs-id1366050\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1807401\">Solve an Equation with Constants on Both Sides<\/h2>\n<p id=\"eip-16\">In the following exercises, solve the equation for the variable.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f6f7df6df793b26c793ddf07e7cde50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#56;&#61;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"91\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f47df311a2b52b9feb9bbc0a3fffc93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#45;&#50;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"91\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-45157637890cbe9bfffac7a40e58d7e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#121;&#43;&#55;&#61;&#57;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-765ace184ce62def89c34219ccce2000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#119;&#43;&#54;&#61;&#57;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"102\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85ab65d5a4a33933a8e315e4fd115664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#43;&#57;&#61;&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"111\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83ce8657c3cf4399af4f02404195d834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#97;&#43;&#56;&#61;&#45;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb1a8edf89f05fbe36f2a9f1bcc8755c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#55;&#61;&#54;&#98;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35788be0382071b27668e6a1ae40b3b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#48;&#61;&#55;&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"103\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae74f56ff9bbdacb0ed9596ee152ad50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#57;&#61;&#45;&#56;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"105\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb7bb33cc2637744b219c5dc5c013a71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#61;&#45;&#57;&#121;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-609c9e068f5b2ce5622836a4d81ab9d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#125;&#45;&#49;&#53;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -3px;\" \/><\/td>\n<td>12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6eca2a7846d9f6509a11f70e6139091a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#112;&#45;&#51;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1494639\">Solve an Equation with Variables on Both Sides<\/h2>\n<p id=\"eip-57\">In the following exercises, solve the equation for the variable.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a44f75df8184c53917812168563e70b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#107;&#61;&#56;&#107;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"100\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85767e90ab955c5870caaab763deb8e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#122;&#61;&#55;&#122;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"90\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d33571f9bbcd92b1a2c138067c35b802_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#50;&#55;&#61;&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f35c30ad236ae6d9370fd9b52b9dc520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#54;&#61;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"110\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-483035e825faa492f96fec43b2874f9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#45;&#52;&#98;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"100\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c98841497cc79b85f543a8086e399d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#45;&#51;&#99;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"101\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02a74a1ec7bdaa8a046e9fe392dd9581_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#122;&#61;&#51;&#57;&#45;&#54;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"99\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-28c06e8c2a771404e168613896f9443a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#113;&#61;&#52;&#52;&#45;&#54;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4fea1c90bf9557179aec57205d62f93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"94\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04a6cd552a97128f3da6c477cfef6578_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"92\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfde698201b92327fa448190ab83bef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#114;&#45;&#56;&#61;&#45;&#49;&#49;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"133\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e3aad2d18d24184d6937dde219a98c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#97;&#45;&#56;&#61;&#45;&#49;&#54;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"135\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166490741372\">Solve an Equation with Variables and Constants on Both Sides<\/h2>\n<p id=\"eip-969\">In the following exercises, solve the equations for the variable.<\/p>\n<table>\n<tbody>\n<tr>\n<td>25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d80c64350e07120460338e0ac9905f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#49;&#55;&#61;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f17c8dc59aadeef1c7c9774f8c2a2f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#45;&#49;&#53;&#61;&#53;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"132\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-13a5e8cb4d2ffd23c047edc913eb1d3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#43;&#54;&#102;&#61;&#55;&#102;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"142\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7dcd2b1100be453988af4fe1bc6dc426_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;&#43;&#56;&#100;&#61;&#57;&#100;&#43;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"138\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7224fa3f1fdb4810d25920b76fbddfff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#113;&#45;&#53;&#61;&#53;&#113;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b9ca2c13f7ffe3872676ed88163e13a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#112;&#45;&#49;&#61;&#53;&#112;&#45;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec9c1a1d80d84b234f0fcd9455ad66a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#99;&#43;&#55;&#61;&#45;&#50;&#99;&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"141\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eaca84efc7715788f00bb7e0e5029e75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#97;&#43;&#53;&#61;&#45;&#97;&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"135\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7bc0a663431e726c102e43bf3c6966f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#45;&#49;&#55;&#61;&#45;&#51;&#120;&#43;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"162\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc53be5e78555b09d8b3f4a95061ae3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#45;&#51;&#48;&#61;&#45;&#50;&#121;&#43;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2763f0622bdfb89fee3df8efc062404b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#45;&#52;&#61;&#49;&#50;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecf008bb9358b3a068156f2ffe43a9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#122;&#125;&#45;&#52;&#61;&#50;&#51;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#122;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"118\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfe71db694daabbbce6259b3a3774695_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#45;&#55;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"148\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c19d48c5942cbffecb257860363c3ba7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#45;&#51;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-45db329ab1d5676ef542c84dd5fd7050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"137\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2836a60ed17a86a8aa916356a0ba7f5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f9fec80d39b9c771c8a76256b63ebd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#43;&#49;&#53;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"135\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ceba49930cb4ac11715d93944d55ecce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#43;&#57;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"129\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-619d5843d58a0d72c609638c7ec9ff57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#43;&#50;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99d6531269cc5489a9ed8d7b6ffdde4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#55;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a4485db25de3eee5af075a9145c94f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#122;&#43;&#54;&#46;&#52;&#53;&#61;&#56;&#122;&#43;&#50;&#51;&#46;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"182\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-304570ca7ebe0a30f47f183195624f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#110;&#43;&#56;&#46;&#50;&#53;&#61;&#57;&#110;&#43;&#49;&#57;&#46;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"186\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9d8f517082f76dac87e6fddb9009219_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#55;&#119;&#45;&#56;&#48;&#61;&#49;&#46;&#50;&#119;&#43;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"174\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49e1fd64589a5d4bc4462e2d012fac4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#52;&#119;&#45;&#49;&#48;&#48;&#61;&#48;&#46;&#56;&#119;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"183\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2838bd03f4a07cf50335672543a59162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#54;&#120;&#45;&#49;&#56;&#46;&#57;&#61;&#51;&#46;&#52;&#120;&#43;&#53;&#52;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa84a339b947c798155e526e993e296d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#54;&#114;&#43;&#49;&#51;&#46;&#49;&#61;&#51;&#46;&#53;&#114;&#43;&#53;&#55;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"192\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1560582\">Solve an Equation Using the General Strategy<\/h2>\n<p id=\"eip-377\">In the following exercises, solve the linear equation using the general strategy.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c736926bad33ef7577ad9989b4c05cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb91e2ca75277029cd854963d57ad8ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b77b90d149c9d292c8314ac5e7e938f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-733580b015ecbac183f818adf2dd9fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#61;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa972cfd4e388d0f42f42c32e33d95eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe0e726903bd7e57e054d79ee4f49e64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f15f4172f08ed331ae6ec06e01cf4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#110;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7db9b2a7773bf298eceabc8f9270230e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2178e2e68f5ee910cb31e12097661f72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecba4dc47c5a9892addd0d01f9349f45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#43;&#53;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c6778206856deacd41e6ca52d0e2465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c8875338505aeab253db3a2d6ba9f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d550d1a74a0b3b748f2fb5e6afc3a9c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#118;&#45;&#48;&#46;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"148\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-873e715d6b3adf08d9f6bf7efedc4c98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#50;&#117;&#45;&#52;&#46;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"157\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26950d791092d7164fa8d0478cba2b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#109;&#43;&#51;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f3813b513aa78145dc3a8d68a96872e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#110;&#43;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-183113cb03ab303781154289b8f75d4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00391cf0ce4f8604b46febe226b110da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca2467a6f0c06cfe5235180afbec52fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#98;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#51;&#61;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd1905fa162f95ccd185782b2f1c4287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;&#61;&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"147\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a85769eb0ea2c6b4807440f176eab9e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-887e1ea3961b68b2528c065b9fb961da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce11c49877e59c6e86c85dece01c3ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#43;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#107;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"150\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e4f697cb38d2f3c0a3bc5293210776f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b5a21fab8b494f1c077c206db56d8d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#114;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"156\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5ada2d7192c97ac8265fb5a144a837c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"142\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2607567980d551526dea46498cd59fd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04f8b0993f8530ceacaa5643b10757d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e30d6516f5be48a6691035690823b22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#61;&#56;&#110;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"180\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6bd54592b9424400016cebde136090a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#112;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"162\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e0ee130adddd011d6e6742062dec91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#120;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1123bf80d5a2074196f796b034eb9cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#52;&#109;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bc95ed554c5cfafa75df5168fca296f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#115;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"244\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20712f96137100709ed6bed0753dd68c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#120;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-228e7c731cbb07a6ada35f53c914b74e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"226\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff63c98a7f9aa005146dea765cae380e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"261\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1732048\" class=\"everyday\" data-depth=\"2\">\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table>\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">Making a fence 87.\u00a0<\/strong> Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74a92b6c533b233c6f544c969f0e81fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet more than the width. Find the width, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6030962ed4c45ee07044aede537d8d34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<td><strong data-effect=\"bold\">Concert tickets<\/strong>\u00a0 88. At a school concert, the total value of tickets sold was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fec327c6620be9cd00301d08f25e0406_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#44;&#53;&#48;&#54;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -4px;\" \/> Student tickets sold for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-155ad90dc8caf91fd0b8f3e9b42c16a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -1px;\" \/> and adult tickets sold for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2be85b09c6d3c8d9747ad0366dd35660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#57;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -1px;\" \/> The number of adult tickets sold was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> times the number of student tickets. Find the number of student tickets sold, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9417e1eb1b2f966eb818077fd46dfcd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#115;&#43;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#53;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"172\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Coins<\/strong> 89. Rhonda has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1254518f4b8ca986f0002a86d6c1a0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#46;&#57;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -1px;\" \/> in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e4db7258a9970cec755689f70ab59f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#110;&#43;&#48;&#46;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#46;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"218\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><strong data-effect=\"bold\">Fencing<\/strong> 90. Micah has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3366680a905e594fe45b1862a7c4ab8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet of fencing to make a rectangular dog pen in his yard. He wants the length to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet more than the width. Find the length, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51af75068f28f939d60ec7da998dc59d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#76;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#76;&#45;&#50;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"161\" style=\"vertical-align: -5px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166483068552\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<div id=\"fs-id1440481\" data-type=\"exercise\">\n<div id=\"fs-id1166491068825\" data-type=\"problem\">\n<table>\n<tbody>\n<tr>\n<td>91. 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?<\/td>\n<td>92. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15684bc154f74ca38bfdd06a6739c728_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#43;&#49;&#52;&#61;&#45;&#50;&#120;&#43;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"162\" style=\"vertical-align: -2px;\" \/>, explaining all the steps of your solution.<\/td>\n<\/tr>\n<tr>\n<td>93. What is the first step you take when solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f9627b8cb39b52d4b9dd60bc6453670_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#56;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"146\" style=\"vertical-align: -4px;\" \/> Explain why this is your first step.<\/td>\n<td>94. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c49fd33350b7a77a5dc7ff9142337942_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#120;&#43;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/> explaining all the steps of your solution as in the examples in this section.<\/td>\n<\/tr>\n<tr>\n<td>95. Using your own words, list the steps in the General Strategy for Solving Linear Equations.<\/td>\n<td>96. 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.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div id=\"fs-id1166470615289\" data-type=\"exercise\">\n<div id=\"fs-id1166479431647\" data-type=\"problem\">\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>1. 6<\/td>\n<td>3.6<\/td>\n<td>5. -8<\/td>\n<\/tr>\n<tr>\n<td>7. -8<\/td>\n<td>9. -4<\/td>\n<td>11. -2<\/td>\n<\/tr>\n<tr>\n<td>13. -11<\/td>\n<td>15. 9<\/td>\n<td>17. -3<\/td>\n<\/tr>\n<tr>\n<td>19. 3<\/td>\n<td>21. -3\/4<\/td>\n<td>25. 19<\/td>\n<\/tr>\n<tr>\n<td>27. 7<\/td>\n<td>29. -5<\/td>\n<td>31. -4<\/td>\n<\/tr>\n<tr>\n<td>33. 2<\/td>\n<td>35. 4<\/td>\n<td>37. -6<\/td>\n<\/tr>\n<tr>\n<td>39. 7<\/td>\n<td>41. -40<\/td>\n<td>43. 15<\/td>\n<\/tr>\n<tr>\n<td>45. 3.46<\/td>\n<td>47. 60<\/td>\n<td>49. 23<\/td>\n<\/tr>\n<tr>\n<td>51. 9<\/td>\n<td>53. 6<\/td>\n<td>55. 3<\/td>\n<\/tr>\n<tr>\n<td>57. \u22122<\/td>\n<td>59. \u22121<\/td>\n<td>61. 5<\/td>\n<\/tr>\n<tr>\n<td>63. 0.52<\/td>\n<td>65. 0.25<\/td>\n<td>67. \u22129<\/td>\n<\/tr>\n<tr>\n<td>69. 2<\/td>\n<td>71. 6<\/td>\n<td>73. 3\/2<\/td>\n<\/tr>\n<tr>\n<td>75. 3<\/td>\n<td>77. \u22124<\/td>\n<td>79. 2<\/td>\n<\/tr>\n<tr>\n<td>81. 34<\/td>\n<td>83. 10<\/td>\n<td>85. 2<\/td>\n<\/tr>\n<tr>\n<td>87. 30 feet<\/td>\n<td>89. 8 nickels<\/td>\n<td>91. Answers will vary.<\/td>\n<\/tr>\n<tr>\n<td>93. Answers will vary.<\/td>\n<td>95. Answers will vary.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSolve Equations with Variables and Constants on Both Sides\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":90,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1042","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1042\/revisions"}],"predecessor-version":[{"id":1043,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1042\/revisions\/1043"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1042\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1042"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1042"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1042"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}