{"id":842,"date":"2020-08-12T14:17:51","date_gmt":"2020-08-12T18:17:51","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-using-the-subtraction-and-addition-properties-of-equality\/"},"modified":"2021-03-24T10:54:48","modified_gmt":"2021-03-24T14:54:48","slug":"solve-equations-using-the-subtraction-and-addition-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-using-the-subtraction-and-addition-properties-of-equality\/","title":{"raw":"5.1 Solve Equations Using the Subtraction and Addition Properties of Equality","rendered":"5.1 Solve Equations Using the Subtraction and Addition Properties of Equality"},"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 equations using the Subtraction and Addition Properties of Equality<\/li>\n \t<li>Solve equations that need to be simplified<\/li>\n \t<li>Translate an equation and solve<\/li>\n \t<li>Translate and solve applications<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1166493765778\">We are now ready to \u201cget to the good stuff.\u201d You have the basics down and are ready to begin one of the most important topics in algebra: solving equations. The applications are limitless and extend to all careers and fields. Also, the skills and techniques you learn here will help improve your critical thinking and problem-solving skills. This is a great benefit of studying mathematics and will be useful in your life in ways you may not see right now.<\/p>\n\n<div id=\"fs-id1956457\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h1>\n<p id=\"fs-id1166497276639\">Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.<\/p>\n\n<div id=\"fs-id1329645\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Solution of an Equation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nA solution of an equation is a value of a variable that makes a true statement when substituted into the equation.\n\n<\/div>\n<\/div>\nThe steps to determine if a value is a solution to an equation are listed here.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Determine whether a number is a solution to an equation.<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-95\" class=\"stepwise\" type=\"1\">\n \t<li>Substitute the number for the variable in the equation.<\/li>\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\n \t<li>Determine whether the resulting equation is true.\n<ul id=\"fs-id1703984\" data-bullet-style=\"bullet\">\n \t<li>If it is true, the number is a solution.<\/li>\n \t<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166492761655\" 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 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1518747\" data-type=\"problem\">\n<p id=\"fs-id1166484083630\">Determine whether \\(y=\\frac{3}{4}\\) is a solution for \\(4y+3=8y\\).<\/p>\n<strong><span style=\"font-size: 0.9em; word-spacing: normal;\">Solution<\/span><\/strong>\n\n<\/div>\n<div id=\"fs-id1166491409809\" data-type=\"solution\">\n<table id=\"eip-id1168466426761\" class=\"unnumbered unstyled\" summary=\"The top line says 4y plus 3 equals 8y. Beside this is \u201cGiven.\u201d The next line says 4 times a red three-fourths plus 3 followed by an equal sign with a question mark, then 8 times a red three-fourths. Beside this is \u201cSubstitute three-fourths for y.\u201d Three-fourths is in red. The next line says 3 plus 3 equal sign with a question mark 6. Beside this is \u201cMultiply.\u201d The last line says 6 equals 6. Beside this is \u201cAdd. The solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468702694\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_01_001_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466078265\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><span id=\"eip-id1168469511022\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468288486\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-04-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1168468655391\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1877457\">Since \\(y=\\frac{3}{4}\\) results in a true equation, \\(\\frac{3}{4}\\) is a solution to the equation \\(4y+3=8y\\).<\/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 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1486889\" data-type=\"problem\">\n<p id=\"fs-id1951701\">Is \\(y=\\frac{2}{3}\\) a solution for \\(9y+2=6y?\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166497326966\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1603913\">no<\/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-id1698735\" data-type=\"problem\">\n<p id=\"fs-id1166484604448\">Is \\(y=\\frac{2}{5}\\) a solution for \\(5y-3=10y?\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166494755266\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166494591269\">no<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nIn that section,we will model how the Subtraction and Addition Properties work and then we will apply them to solve equations.\n\n<\/div>\n<\/div>\n<div id=\"fs-id1731715\" data-type=\"note\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction Property of Equality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFor all real numbers \\(a,b\\), and \\(c\\), if \\(a=b\\), then \\(a-c=b-c\\).\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Addition Property of Equality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFor all real numbers \\(a,b\\), and \\(c\\), if \\(a=b\\), then \\(a+c=b+c\\).\n\n<\/div>\n<\/div>\n<p id=\"fs-id1166497417158\">When you add or subtract the same quantity from both sides of an equation, you still have equality.<\/p>\n\n<\/div>\n<p id=\"eip-108\">We will introduce the <span class=\"no-emphasis\" data-type=\"term\">Subtraction Property of Equality<\/span>\u00a0by modeling equations with envelopes and counters. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_08_01_026\">(Figure .1)<\/a> models the equation \\(x+3=8\\).<\/p>\n\n<div id=\"CNX_BMath_Figure_08_01_026\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"211\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_026-2.jpg\" alt=\"An envelope and three yellow counters are shown on the left side. On the right side are eight yellow counters.\" width=\"211\" height=\"129\" data-media-type=\"image\/jpeg\"> Figure .1[\/caption]\n\n<\/div>\n<p id=\"fs-id1856746\">The goal is to isolate the variable on one side of the equation. So we \u2018took away\u2019 \\(3\\) from both sides of the equation and found the <span class=\"no-emphasis\" data-type=\"term\">solution<\/span> \\(x=5\\).<\/p>\n<p id=\"fs-id1166490921090\">Some people picture a balance scale, as in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_08_01_001\">(Figure .2)<\/a>, when they solve equations.<\/p>\n\n<div id=\"CNX_BMath_Figure_08_01_001\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"476\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001-2.jpg\" alt=\"Three balance scales are shown. The top scale has one red weight on each side and is balanced. Beside it is \u201c1 mass on each side equals balanced.\u201d The next scale has two weights on each side and is balanced. Beside it is \u201c2 masses on each side equals balanced.\u201d The bottom scale has one weight on the left and two on the right. The right side is lower than the left. Beside the image is \u201c1 mass on one side and 2 masses on the other equals unbalanced.\u201d\" width=\"476\" height=\"500\" data-media-type=\"image\/jpeg\"> Figure .2[\/caption]\n\n<\/div>\n<p id=\"fs-id1166497425012\">The quantities on both sides of the equal sign in an equation are equal, or balanced. Just as with the balance scale, whatever you do to one side of the equation you must also do to the other to keep it balanced.<\/p>\n<p id=\"fs-id1166491428047\">Let\u2019s see how to use Subtraction and Addition Properties of Equality to solve equations. We need to isolate the variable on one side of the equation. And we check our solutions by substituting the value into the equation to make sure we have a true statement.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1953663\" data-type=\"problem\">\n<p id=\"fs-id1736543\">Solve: \\(x+11=-3\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166488297178\" data-type=\"solution\">\n<p id=\"fs-id1487471\">To isolate \\(x\\), we undo the addition of \\(11\\) by using the Subtraction Property of Equality.<\/p>\n\n<table id=\"eip-id1168468291100\" style=\"width: 100%;\" summary=\"The top line says x plus 11 equals negative 3. The next line says, \u201cSubtract 11 from each side, to 'undo' the addition.\u201d Beside this is x plus 11 minus a red 11 equals negative 3 minus a red 11. The next line says \u201csimplify.\u201d Beside this is x equals negative 14. The next line says \u201ccheck.\u201d Beside this is x plus 11 equals negative 3. The last line says \u201csubstitute\u201d and shows x equals negative 14, then a red negative 14 plus 11 followed by an equal sign with a question mark and a negative 3, then negative 3 equals negative 3 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168469834553\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Subtract 11 from each side to \"undo\" the addition.<\/td>\n<td><span id=\"eip-id1168466137434\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168466092262\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168466072125\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-04-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute \\(x=-14\\).<\/td>\n<td><span id=\"eip-id1168466079144\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469869298\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-06-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1468740\">Since \\(x=-14\\) makes \\(x+11=-3\\) a true statement, we know that it is a solution to the equation.<\/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 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493722919\" data-type=\"problem\">\n<p id=\"fs-id900542\">Solve: \\(x+9=-7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166492788206\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166497163046\"><em data-effect=\"italics\">x<\/em> = \u221216<\/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-id1944892\" data-type=\"problem\">\n<p id=\"fs-id1166491429192\">Solve: \\(x+16=-4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166493761190\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166491084479\"><em data-effect=\"italics\">x<\/em> = \u221220<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166490870130\">In the original equation in the previous example, \\(11\\) was added to the \\(x\\), so we subtracted \\(11\\) to \u2018undo\u2019 the addition. In the next example, we will need to \u2018undo\u2019 subtraction by using the <span class=\"no-emphasis\" data-type=\"term\">Addition Property of Equality<\/span>.<\/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-id1166479028976\" data-type=\"problem\">\n<p id=\"fs-id1511517\">Solve: \\(m-4=-5\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166478988064\" data-type=\"solution\">\n<table id=\"eip-id1168467157298\" style=\"width: 100%;\" summary=\"The first line says m minus 4 equals negative 5. The next line says, \u201cAdd 4 to each side, to 'undo' the subtraction.\u201d Beside this is m minus 4 plus a red 4 equals negative 5 plus a red 4. The next line says \u201csimplify\u201d and shows m equals negative 1. The following line says to \u201ccheck\u201d and shows m minus 4 equals negative 5. Below this is \u201csubstitute\u201d and m equals negative 1. Below that is a red negative 1 minus 4 followed by an equal sign with a question mark and negative 5. The last line shows negative 5 equals negative 5 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468473383\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add 4 to each side to \"undo\" the subtraction.<\/td>\n<td><span id=\"eip-id1168467340413\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467332056\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468552729\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-04-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute \\(m=-1\\).<\/td>\n<td><span id=\"eip-id1168468614495\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467261089\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-06-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>The solution to \\(m-4=-5\\) is \\(m=-1\\).<\/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-id1508126\" data-type=\"problem\">\n<p id=\"fs-id1166493484246\">Solve: \\(n-6=-7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491411267\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166490916413\">\u22121<\/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 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491003339\" data-type=\"problem\">\n<p id=\"fs-id1166491256493\">Solve: \\(x-5=-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1485263\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1482600\">\u22124<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1486893\">Now let\u2019s\u00a0 solve equations with fractions.<\/p>\n\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 data-type=\"problem\">\n<p id=\"fs-id1806883\">Solve: \\(n-\\frac{3}{8}=\\frac{1}{2}\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166494770805\" data-type=\"solution\">\n<table id=\"eip-id1168468255179\" style=\"width: 100%;\" summary=\"The first line says n minus 3 eighths equals one half. The next line says, \u201cUse the Addition Property of Equality.\u201d Beside this is n minus 3 over 8 plus a red 3 over 8 equals one half plus a red 3 over 8. The next line says \u201cFind the LCD to add the fractions on the right.\u201d Beside that is n minus 3 over 8 plus 3 over 8 equals 4 over 8 plus 3 over 8. The next line says \u201csimplify\u201d and shows n equals 7 over 8. Below that is \u201ccheck\u201d and n minus 3 eighths equals one half. The following line says to substitute n equals 7 over 8 and shows a red 7 over 8 minus 3 over 8 followed by an equal sign with a question mark and one half. The next line says \u201csubtract\u201d and shows 4 over 8, equal sign with a question mark, 1 half. The last line says \u201csimplify\u201d and says one half equals one half with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168466176178\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168469603754\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Find the LCD to add the fractions on the right.<\/td>\n<td><span id=\"eip-id1168469611733\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify<\/td>\n<td><span id=\"eip-id1168469683726\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168466175504\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468241254\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><span id=\"eip-id1168467114144\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168469872572\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469615789\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/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-id2050763\" data-type=\"problem\">\n<p id=\"fs-id1430998\">Solve: \\(p-\\frac{1}{3}=\\frac{5}{6}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1455960\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166491425616\">\\(p=\\frac{7}{6}\\)<\/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-id1166493722928\" data-type=\"problem\">\n<p id=\"fs-id1449225\">Solve: \\(q-\\frac{1}{2}=\\frac{1}{6}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1798095\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1766639\">\\(q=\\frac{2}{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166482443040\">Let's solve equations that contained decimals.<\/p>\n\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-id1166497408110\" data-type=\"problem\">\n<p id=\"fs-id1166490790049\">Solve \\(a-3.7=4.3\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1736242\" data-type=\"solution\">\n<table id=\"eip-id1168468751492\" style=\"width: 100%;\" summary=\"The top line says a minus 3.7 equals 4.3. The next line says \u201cUse the Addition Property of Equality.\u201d Beside that is a minus 3.7 plus a red 3.7 equals 4.3 plus a red 3.7. The next line says to add and shows a equals 8. The next line says to check and shows a minus 3.7 equals 4.3. Below that is \u201cSubstitute a equals 8\u201d and a red 8 minus 3.7 followed by an equal sign with a question mark and 4.3. The last line says to simplify and shows 4.3 equals 4.3 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168467170715\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168468232824\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add.<\/td>\n<td><span id=\"eip-id1168468412922\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468389351\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute \\(a=8\\).<\/td>\n<td><span id=\"eip-id1168465145363\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468520006\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/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-id1357810\" data-type=\"problem\">\n<p id=\"fs-id1166492771569\">Solve: \\(b-2.8=3.6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166484109037\" data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">b<\/em> = 6.4\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 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1768687\" data-type=\"problem\">\n<p id=\"fs-id1249306\">Solve: \\(c-6.9=7.1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1418529\" data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">c<\/em> = 14\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations That Need to Be Simplified<\/h1>\n<\/div>\n<div id=\"fs-id1471572\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166494591280\">In the examples up to this point, we have been able to isolate the variable with just one operation. Many of the equations we encounter in algebra will take more steps to solve. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality. You should always simplify as much as possible before trying to isolate the variable.<\/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-id1693654\" data-type=\"problem\">\n\nSolve: \\(3x-7-2x-4=1\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1475828\" data-type=\"solution\">\n<p id=\"fs-id1495618\">The left side of the equation has an expression that we should simplify before trying to isolate the variable.<\/p>\n\n<table id=\"eip-id1168467171254\" style=\"height: 286px; width: 100%;\" summary=\"The first line shows the equation 3x minus 7 minus 2x minus 4 equals 1. The next line says, \u201cRearrange the terms, using the Commutative Property of Addition.\u201d Beside this is 3x minus 2x minus 7 minus 4 equals 1. The next line says, \u201cCombine like terms.\u201d Beside this is x minus 11 equals 1. The next line says, \u201cAdd 11 to both sides to isolate x.\u201d Beside this is x minus 11 plus a red 11 equals 1 plus a red 11. The last line says \u201csimplify\u201d and shows x equals 12.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px; width: 411.25px;\"><\/td>\n<td style=\"height: 24px; width: 198.75px;\"><span id=\"eip-id1168468454842\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 411.25px;\">Rearrange the terms, using the Commutative Property of Addition.<\/td>\n<td style=\"height: 22px; width: 198.75px;\"><span id=\"eip-id1168468592120\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 411.25px;\">Combine like terms.<\/td>\n<td style=\"height: 23px; width: 198.75px;\"><span id=\"eip-id1168468458434\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 411.25px;\">Add 11 to both sides to isolate \\(x\\).<\/td>\n<td style=\"height: 23px; width: 198.75px;\"><span id=\"eip-id1168467375475\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 411.25px;\">Simplify.<\/td>\n<td style=\"height: 22px; width: 198.75px;\"><span id=\"eip-id1168468451956\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 172px;\">\n<td style=\"height: 172px; width: 411.25px;\">Check.\nSubstitute \\(x=12\\) into the original equation.\n<span id=\"fs-id1480549\" data-type=\"media\" data-alt=\"The top line shows 3x minus 7 minus 2x minus 4 equals 1. Below this is 3 times a red 12 minus 7 minus 2 times a red 12 minus 4 equals 1. Next is 36 minus 7 minus 24 minus 4 equals 1. Below is 29 minus 24 minus 4 equals 1. Next is 5 minus 4 equals 1. Last is 1 equals 1.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_011_img-1.jpg\" alt=\"The top line shows 3x minus 7 minus 2x minus 4 equals 1. Below this is 3 times a red 12 minus 7 minus 2 times a red 12 minus 4 equals 1. Next is 36 minus 7 minus 24 minus 4 equals 1. Below is 29 minus 24 minus 4 equals 1. Next is 5 minus 4 equals 1. Last is 1 equals 1.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"height: 172px; width: 198.75px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1303501\">The solution checks.<\/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 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1241927\" data-type=\"problem\">\n<p id=\"fs-id1731867\">Solve: \\(8y-4-7y-7=4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1502572\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166476201528\"><em data-effect=\"italics\">y<\/em> = 15<\/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 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1733102\" data-type=\"problem\">\n<p id=\"fs-id1437081\">Solve: \\(6z+5-5z-4=3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1357223\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166491297361\"><em data-effect=\"italics\">z<\/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 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547337\" data-type=\"problem\">\n<p id=\"fs-id1166497425790\">Solve: \\(3\\left(n-4\\right)-2n=-3\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492887596\" data-type=\"solution\">\n<p id=\"fs-id1302362\">The left side of the equation has an expression that we should simplify.<\/p>\n\n<table id=\"eip-id1168468254328\" style=\"width: 100%;\" summary=\"The top line says \u201cgiven\u201d and shows 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says \u201cdistribute on the left\u201d and shows 3n minus 12 minus 2n equals negative 3. The next line says, \u201cUse the Commutative Property to rearrange terms.\u201d Beside this is 3n minus 2n minus 12 equals negative 3. The next step says \u201cCombine like terms.\u201d Beside this is n minus 12 equals negative 3. The next line says, \u201cIsolate n using the Addition Property of Equality.\u201d Beside this is n minus 12 plus a red 12 equals negative 3 plus a red 12. The last line says \u201csimplify\u201d and shows n equals 9.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468249958\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute on the left.<\/td>\n<td><span id=\"eip-id1168468557711\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange terms.<\/td>\n<td><span id=\"eip-id1168467473331\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168467453602\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Isolate <em data-effect=\"italics\">n<\/em> using the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168468554542\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_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-id1168468358150\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.\nSubstitute \\(n=9\\) into the original equation.\n<span id=\"fs-id1494005\" data-type=\"media\" data-alt=\"The top line says 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says 3 times parentheses red 9 minus 3 minus 2 times red 9 equals negative 3. The next line says 3 times 5 minus 18 equals negative 3. Below this is 15 minus 18 equals negative 3. Last is negative 3 equals negative 3.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_013_img-1.jpg\" alt=\"The top line says 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says 3 times parentheses red 9 minus 3 minus 2 times red 9 equals negative 3. The next line says 3 times 5 minus 18 equals negative 3. Below this is 15 minus 18 equals negative 3. Last is negative 3 equals negative 3.\" data-media-type=\"image\/jpeg\"><\/span>\nThe solution checks.<\/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 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491296425\" data-type=\"problem\">\n<p id=\"fs-id834398\">Solve: \\(5\\left(p-3\\right)-4p=-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1444663\" data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">p<\/em> = 5\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 id=\"fs-id1166498049515\" data-type=\"problem\">\n<p id=\"fs-id1242285\">Solve: \\(4\\left(q+2\\right)-3q=-8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491403679\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1491162\"><em data-effect=\"italics\">q<\/em> = \u221216<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id834918\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166484082143\" data-type=\"exercise\">\n<div id=\"fs-id1166491296425\" 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-id1166493761721\" data-type=\"problem\">\n<p id=\"fs-id1724676\">Solve: \\(2\\left(3k-1\\right)-5k=-2-7\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166483694459\" data-type=\"solution\">\n\nBoth sides of the equation have expressions that we should simplify before we isolate the variable.\n<table id=\"eip-id1168469785088\" style=\"width: 100%;\" summary=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. The next line says \u201cDistribute on the left, subtract on the right.\u201d Beside that is 6k minus 2 minus 5k equals negative 9. The next line says \u201cUse the Commutative Property of Addition.\u201d Beside that is 6k minus 5k minus 2 equals negative 9. The next step says \u201ccombine like terms\u201d and shows k minus 2 equals negative 9. The next step says, \u201cUndo subtraction by using the Addition Property of Equality.\u201d Beside that is k minus 2 plus a red 2 equals negative 9 plus a red 2. The last step says to simplify and shows k equals negative 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466140979\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute on the left, subtract on the right.<\/td>\n<td><span id=\"eip-id1168469711596\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property of Addition.<\/td>\n<td><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469577466\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Undo subtraction by using the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168469699676\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_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-id1168466203200\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check. Let \\(k=-7\\).<\/td>\n<td><span id=\"eip-id1168466203200\" data-type=\"media\" data-alt=\".\"><span data-type=\"media\" data-alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_014_img-1.jpg\" alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><span id=\"eip-id1168466203200\" data-type=\"media\" data-alt=\".\"><span data-type=\"media\" data-alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\">\u00a0<\/span><\/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 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1317627\" data-type=\"exercise\">\n<div id=\"fs-id1457105\" data-type=\"problem\">\n<p id=\"fs-id1877708\">Solve: \\(4\\left(2h-3\\right)-7h=-6-7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1388025\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1500361\"><em data-effect=\"italics\">h<\/em> = \u22121<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/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-id1496617\" data-type=\"problem\">\n<p id=\"fs-id1166494737777\">Solve: \\(2\\left(5x+2\\right)-9x=-2+7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1956094\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1526415\"><em data-effect=\"italics\">x<\/em> = 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Translate an Equation and Solve<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1580769\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166488299698\">Previously, we translated word sentences into equations. The first step is to look for the word (or words) that translate(s) to the equal sign. The list below reminds us of some of the words that translate to the equal sign (=):<\/p>\n\n<ul>\n \t<li>is<\/li>\n \t<li>is equal to<\/li>\n \t<li>is the same as<\/li>\n \t<li>the result is<\/li>\n \t<li>gives<\/li>\n \t<li>was<\/li>\n \t<li>will be<\/li>\n<\/ul>\nLet\u2019s review the steps we used to translate a sentence into an equation.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Translate a word sentence to an algebraic equation.<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-112\" class=\"stepwise\" type=\"1\">\n \t<li>Locate the \"equals\" word(s). Translate to an equal sign.<\/li>\n \t<li>Translate the words to the left of the \"equals\" word(s) into an algebraic expression.<\/li>\n \t<li>Translate the words to the right of the \"equals\" word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1314958\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n\nNow we are ready to try an example.\n\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-id1166491761371\" data-type=\"problem\">\n\nTranslate and solve: five more than \\(x\\) is equal to \\(26\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168466284401\" style=\"width: 100%;\" summary=\"The first line says \u201cFive more than x is equal to 26.\u201d The next line says \u201ctranslate\u201d and shows x plus 5 equals 26. The next line says \u201csubtract 5 from both sides,\u201d and shows x plus 5 minus a red 5 equals 26 minus a red 5. The next line says to simplify and shows x equals 21. The last step says \u201cCheck. Is 26 five more than 21?\u201d Below that is 21 plus 5, equal sign with a question mark, 26. Then, 26 equals 26 and a check mark. Below that, \u201cThe solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168466049464\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides.<\/td>\n<td><span id=\"eip-id1168469761474\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_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-id1168469866749\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Is \\(26\\) five more than \\(21\\)?<\/td>\n<td><span id=\"eip-id1168466312585\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469622050\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\nThe solution checks.<\/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-id1166476201092\" data-type=\"problem\">\n<p id=\"fs-id1491170\">Translate and solve: Eleven more than \\(x\\) is equal to \\(41\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166498082806\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1505239\"><em data-effect=\"italics\">x<\/em> + 11 = 41; <em data-effect=\"italics\">x<\/em> = 30<\/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-id1508494\" data-type=\"problem\">\n<p id=\"fs-id1166494584879\">Translate and solve: Twelve less than \\(y\\) is equal to \\(51\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1526438\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1335207\"><em data-effect=\"italics\">y<\/em> \u2212 12 = 51; <em data-effect=\"italics\">y<\/em> = 63<\/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 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547575\" data-type=\"problem\">\n<p id=\"fs-id1166483685755\">Translate and solve: The difference of \\(5p\\) and \\(4p\\) is \\(23\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1768035\" data-type=\"solution\">\n<table id=\"eip-id1168468483860\" style=\"width: 100%;\" summary=\"The first line says \u201cThe top line says \u201cTranslate.\u201d Beside that is \u201cThe difference of 5p and 4p is 23.\u201d Below \u201cthe difference of 5p and 4p\u201d is 5p minus 4p. Below \u201cis\u201d is an equal sign. Below 23 is 23. The next line says \u201csimplify\u201d and says p equals 23. The next line says \u201ccheck\u201d and shows 5p minus 4p equals 23. Below that is 5 times 23 minus 4 times 23 equal sign with a question mark 23. The next line says 23 times parentheses 5 minus 4 equal sign with a question mark 23. The next line says 23 times 1 equal sign with a question mark 23. The last line shows 23 equals 23 and says \u201cThe solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168466163340\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466233449\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.\n<span id=\"eip-id1168469741227\" data-type=\"media\" data-alt=\".\"><\/span><\/td>\n<td><span id=\"eip-id1168469511332\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168466231412\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469873016\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469741227\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id830325\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1365772\" data-type=\"exercise\">\n<div id=\"fs-id1526438\" data-type=\"solution\">\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-id1166479044245\" data-type=\"problem\">\n<p id=\"fs-id1456338\">Translate and solve: The difference of \\(4x\\) and \\(3x\\) is \\(14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1456603\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1479670\">4<em data-effect=\"italics\">x<\/em> \u2212 3<em data-effect=\"italics\">x<\/em> = 14; <em data-effect=\"italics\">x<\/em> = 14<\/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-id1538802\" data-type=\"problem\">\n<p id=\"fs-id847862\">Translate and solve: The difference of \\(7a\\) and \\(6a\\) is \\(-8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1494370\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1484361\">7<em data-effect=\"italics\">a<\/em> \u2212 6<em data-effect=\"italics\">a<\/em> = \u22128; <em data-effect=\"italics\">a<\/em> = \u22128<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1454996\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Translate and Solve Applications<\/h1>\n<p id=\"fs-id1166491265463\">In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We\u2019ll start by restating the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.<\/p>\n\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-id1542722\" data-type=\"problem\">\n<p id=\"fs-id1166491402029\">The Robles family has two dogs, Buster and Chandler. Together, they weigh \\(71\\) pounds.<\/p>\n<p id=\"fs-id1505848\">Chandler weighs \\(28\\) pounds. How much does Buster weigh?<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1487807\" data-type=\"solution\">\n<table id=\"eip-id1168468537406\" class=\"unnumbered unstyled\" style=\"width: 471px; height: 238px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">Read the problem carefully.<\/td>\n<td style=\"width: 269.406px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Identify what you are asked to find, and choose a variable to represent it.<\/td>\n<td style=\"width: 269.406px; height: 30px;\">How much does Buster weigh?\nLet \\(b=\\) Buster's weight<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">Write a sentence that gives the information to find it.<\/td>\n<td style=\"width: 269.406px; height: 14px;\">Buster's weight plus Chandler's weight equals 71 pounds.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">We will restate the problem, and then include the given information.<\/td>\n<td style=\"width: 269.406px; height: 14px;\">Buster's weight plus 28 equals 71.<\/td>\n<\/tr>\n<tr style=\"height: 29px;\">\n<td style=\"width: 171.406px; height: 29px;\">Translate the sentence into an equation, using the variable \\(b\\).<\/td>\n<td style=\"width: 269.406px; height: 29px;\"><span id=\"eip-id1168468704181\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 49px;\">\n<td style=\"width: 171.406px; height: 49px;\" data-valign=\"top\">Solve the equation using good algebraic techniques.<\/td>\n<td style=\"width: 269.406px; height: 49px;\"><span id=\"eip-id1168467446215\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168467446225\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Check the answer in the problem and make sure it makes sense.<\/td>\n<td style=\"width: 269.406px; height: 30px;\">Is 43 pounds a reasonable weight for a dog? Yes. Does Buster's weight plus Chandler's weight equal 71 pounds?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\"><\/td>\n<td style=\"width: 269.406px; height: 14px;\" data-align=\"center\">\\(43+28\\stackrel{?}{=}71\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\" data-align=\"center\"><\/td>\n<td style=\"width: 269.406px; height: 14px;\" data-align=\"center\">\\(71=71\\phantom{\\rule{0.2em}{0ex}}\\)\u2713<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Write a complete sentence that answers the question, \"How much does Buster weigh?\"<\/td>\n<td style=\"width: 269.406px; height: 30px;\">Buster weighs 43 pounds<\/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-id1166493492477\" data-type=\"problem\">\n<p id=\"fs-id1166479044410\">Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh \\(13\\) pounds. Zeus weighs \\(6\\) pounds. How much does Athena weigh?<\/p>\n\n<\/div>\n<div id=\"fs-id1508911\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1788943\"><em data-effect=\"italics\">a<\/em> + 6 = 13; Athena weighs 7 pounds.<\/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 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1877445\" data-type=\"problem\">\n<p id=\"fs-id1342552\">Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have \\(68\\) books. Sam has \\(26\\) books. How many books does Henry have?<\/p>\n\n<\/div>\n<div id=\"fs-id1691302\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166497212257\">26 + <em data-effect=\"italics\">h<\/em> = 68; Henry has 42 books.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Devise a Problem-Solving Strategy<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168469608282\" class=\"stepwise\" type=\"1\">\n \t<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n \t<li>Identify what you are looking for.<\/li>\n \t<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n \t<li>Solve the equation using good algebra techniques.<\/li>\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\n \t<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1500299\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166492772961\" data-type=\"exercise\">\n<div id=\"fs-id1166493492477\" data-type=\"problem\">\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-id1555567\" data-type=\"problem\">\n<p id=\"fs-id1505680\">Shayla paid \\(\\text{\\$24,575}\\) for her new car. This was \\(\\text{\\$875}\\) less than the sticker price. What was the sticker price of the car?<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492477793\" data-type=\"solution\">\n<table id=\"eip-id1168469715820\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>\"What was the sticker price of the car?\"<\/td>\n<\/tr>\n<tr>\n<td>Assign a variable.<\/td>\n<td>Let \\(s=\\) the sticker price of the car.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>\\$24,575 is \\$875 less than the sticker price\n\\$24,575 is \\$875 less than \\(s\\)<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1168469875413\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve.<\/td>\n<td><span id=\"eip-id1168469781730\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469577361\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>Is \\$875 less than \\$25,450 equal to \\$24,575?\n\n\\(25,450-875\\stackrel{?}{=}24,575\\)\n\n\\(24,575=24,575\\phantom{\\rule{0.2em}{0ex}}\\)\u2713<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that answers the question.<\/td>\n<td>The sticker price was \\$25,450.<\/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 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166478995641\" data-type=\"problem\">\n<p id=\"fs-id1166497147158\">Translate into an algebraic equation and solve: Eddie paid \\(\\text{\\$19,875}\\) for his new car. This was \\(\\text{\\$1,025}\\) less than the sticker price. What was the sticker price of the car?<\/p>\n\n<\/div>\n<div id=\"fs-id1166497360359\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1416179\">19,875 = <em data-effect=\"italics\">s<\/em> \u2212 1025; the sticker price is \\$20,900.<\/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 id=\"fs-id1166492076305\" data-type=\"problem\">\n<p id=\"fs-id1514129\">Translate into an algebraic equation and solve: The admission price for the movies during the day is \\(\\text{\\$7.75}\\). This is \\(\\text{\\$3.25}\\) less than the price at night. How much does the movie cost at night?<\/p>\n\n<\/div>\n<div id=\"fs-id1511804\" data-type=\"solution\"><details><summary>Show answer<\/summary>7.75 = <em data-effect=\"italics\">n<\/em> \u2212 3.25; the price at night is \\$11.00.\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1443773\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1233682\" data-type=\"exercise\">\n<div id=\"fs-id1166478995641\" data-type=\"problem\">\n<ul id=\"eip-937\">\n \t<li><strong>Determine whether a number is a solution to an equation.<\/strong>\n<ol id=\"eip-id1170325336254\" class=\"stepwise\" type=\"1\">\n \t<li>Substitute the number for the variable in the equation.<\/li>\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\n \t<li>Determine whether the resulting equation is true.<\/li>\n<\/ol>\nIf it is true, the number is a solution.\nIf it is not true, the number is not a solution.<\/li>\n \t<li><strong>Subtraction and Addition Properties of Equality<\/strong>\n<ul id=\"eip-id1170322764024\">\n \t<li><strong>Subtraction Property of Equality<\/strong>\nFor all real numbers <em data-effect=\"italics\">a, b,<\/em> and <em data-effect=\"italics\">c<\/em>,\nif <em data-effect=\"italics\">a = b<\/em> then \\(a-c=b-c\\).<\/li>\n \t<li><strong>Addition Property of Equality<\/strong>\nFor all real numbers <em data-effect=\"italics\">a, b,<\/em> and <em data-effect=\"italics\">c<\/em>,\nif <em data-effect=\"italics\">a = b<\/em> then \\(a+c=b+c\\).<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Translate a word sentence to an algebraic equation.<\/strong>\n<ol id=\"eip-id1170324011027\" class=\"stepwise\" type=\"1\">\n \t<li>Locate the \u201cequals\u201d word(s). Translate to an equal sign.<\/li>\n \t<li>Translate the words to the left of the \u201cequals\u201d word(s) into an algebraic expression.<\/li>\n \t<li>Translate the words to the right of the \u201cequals\u201d word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong>Problem-solving strategy<\/strong>\n<ol id=\"eip-id1170325411872\" class=\"stepwise\" type=\"1\">\n \t<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n \t<li>Identify what you are looking for.<\/li>\n \t<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n \t<li>Solve the equation using good algebra techniques.<\/li>\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\n \t<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1170326208984\">\n \t<dt>solution of an equation<\/dt>\n \t<dd id=\"fs-id1170323908665\">A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<div id=\"fs-id1946531\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1495611\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h2>\n<p id=\"eip-551\">In the following exercises, determine whether the given value is a solution to the equation.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>1. Is \\(y=\\frac{1}{3}\\) a solution of \\(4y+2=10y?\\)<\/td>\n<td>2. Is \\(x=\\frac{3}{4}\\) a solution of \\(5x+3=9x?\\)<\/td>\n<\/tr>\n<tr>\n<td>3. Is \\(u=-\\frac{1}{2}\\) a solution of \\(8u-1=6u?\\)<\/td>\n<td>4. Is \\(v=-\\frac{1}{3}\\) a solution of \\(9v-2=3v?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1770916\">In the following exercises, solve each equation.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>5. \\(x+7=12\\)<\/td>\n<td>6. \\(y+5=-6\\)<\/td>\n<\/tr>\n<tr>\n<td>7. \\(b+\\frac{1}{4}=\\frac{3}{4}\\)<\/td>\n<td>8. \\(a+\\frac{2}{5}=\\frac{4}{5}\\)<\/td>\n<\/tr>\n<tr>\n<td>9. \\(p+2.4=-9.3\\)<\/td>\n<td>10. \\(m+7.9=11.6\\)<\/td>\n<\/tr>\n<tr>\n<td>11. \\(a-3=7\\)<\/td>\n<td>12. \\(m-8=-20\\)<\/td>\n<\/tr>\n<tr>\n<td>13. \\(x-\\frac{1}{3}=2\\)<\/td>\n<td>14. \\(x-\\frac{1}{5}=4\\)<\/td>\n<\/tr>\n<tr>\n<td>15. \\(y-3.8=10\\)<\/td>\n<td>16. \\(y-7.2=5\\)<\/td>\n<\/tr>\n<tr>\n<td>17. \\(x-15=-42\\)<\/td>\n<td>18. \\(z+5.2=-8.5\\)<\/td>\n<\/tr>\n<tr>\n<td>19. \\(q+\\frac{3}{4}=\\frac{1}{2}\\)<\/td>\n<td>20. \\(p-\\frac{2}{5}=\\frac{2}{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1944060\">Solve Equations that Need to be Simplified<\/h2>\n<p id=\"eip-244\">In the following exercises, solve each equation.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>21. \\(m+6-8=15\\)<\/td>\n<td>22. \\(c+3-10=18\\)<\/td>\n<\/tr>\n<tr>\n<td>23. \\(6x+8-5x+16=32\\)<\/td>\n<td>24. \\(9x+5-8x+14=20\\)<\/td>\n<\/tr>\n<tr>\n<td>25. \\(-8n-17+9n-4=-41\\)<\/td>\n<td>26. \\(-6x-11+7x-5=-16\\)<\/td>\n<\/tr>\n<tr>\n<td>27. \\(4\\left(y-2\\right)-3y=-6\\)<\/td>\n<td>28. \\(3\\left(y-5\\right)-2y=-7\\)<\/td>\n<\/tr>\n<tr>\n<td>29. \\(5\\left(w+2.2\\right)-4w=9.3\\)<\/td>\n<td>30. \\(8\\left(u+1.5\\right)-7u=4.9\\)<\/td>\n<\/tr>\n<tr>\n<td>31. \\(-8\\left(x-1\\right)+9x=-3+9\\)<\/td>\n<td>32. \\(-5\\left(y-2\\right)+6y=-7+4\\)<\/td>\n<\/tr>\n<tr>\n<td>33. \\(2\\left(8m+3\\right)-15m-4=3-5\\)<\/td>\n<td>34. \\(3\\left(5n-1\\right)-14n+9=1-2\\)<\/td>\n<\/tr>\n<tr>\n<td>35. \\(-\\left(k+7\\right)+2k+8=7\\)<\/td>\n<td>36. \\(-\\left(j+2\\right)+2j-1=5\\)<\/td>\n<\/tr>\n<tr>\n<td>37. \\(8c-7\\left(c-3\\right)+4=-16\\)<\/td>\n<td>38. \\(6a-5\\left(a-2\\right)+9=-11\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id679510\">Translate to an Equation and Solve<\/h2>\n<p id=\"eip-947\">In the following exercises, translate to an equation and then solve.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>39. The sum of \\(x\\) and \\(-5\\) is \\(33\\).<\/td>\n<td>40.Five more than \\(x\\) is equal to \\(21\\).<\/td>\n<\/tr>\n<tr>\n<td>41.Three less than \\(y\\) is \\(-19\\).<\/td>\n<td>42. Ten less than \\(m\\) is \\(-14\\).<\/td>\n<\/tr>\n<tr>\n<td>43. Eight more than \\(p\\) is equal to \\(52\\).<\/td>\n<td>44. The sum of \\(y\\) and \\(-3\\) is \\(40\\).<\/td>\n<\/tr>\n<tr>\n<td>45. The difference of \\(5c\\) and \\(4c\\) is \\(60\\).<\/td>\n<td>46. The difference of \\(9x\\) and \\(8x\\) is \\(17\\).<\/td>\n<\/tr>\n<tr>\n<td>47. The difference of \\(f\\) and \\(\\frac{1}{3}\\) is \\(\\frac{1}{12}\\).<\/td>\n<td>48. The difference of \\(n\\) and \\(\\frac{1}{6}\\) is \\(\\frac{1}{2}\\).<\/td>\n<\/tr>\n<tr>\n<td>49. The sum of \\(-9m\\) and \\(10m\\) is \\(-25\\).<\/td>\n<td>50. The sum of \\(-4n\\) and \\(5n\\) is \\(-32\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166488297752\">Translate and Solve Applications<\/h2>\nIn the following exercises, translate into an equation and solve.\n<table border=\"0\">\n<tbody>\n<tr>\n<td>51.Jeff read a total of \\(54\\) pages in his English and Psychology textbooks. He read \\(41\\) pages in his English textbook. How many pages did he read in his Psychology textbook?<\/td>\n<td>52. Pilar drove from home to school and then to her aunt\u2019s house, a total of \\(18\\) miles. The distance from Pilar\u2019s house to school is \\(7\\) miles. What is the distance from school to her aunt\u2019s house?<\/td>\n<\/tr>\n<tr>\n<td>53. Eva\u2019s daughter is \\(5\\) years younger than her son. Eva\u2019s son is \\(12\\) years old. How old is her daughter?<\/td>\n<td>54. Pablo\u2019s father is \\(3\\) years older than his mother. Pablo\u2019s mother is \\(42\\) years old. How old is his father?<\/td>\n<\/tr>\n<tr>\n<td>55. For a family birthday dinner, Celeste bought a turkey that weighed \\(5\\) pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed \\(16\\) pounds. How much did the Thanksgiving turkey weigh?<\/td>\n<td>56. Allie weighs \\(8\\) pounds less than her twin sister Lorrie. Allie weighs \\(124\\) pounds. How much does Lorrie weigh?<\/td>\n<\/tr>\n<tr>\n<td>57. Connor\u2019s temperature was \\(0.7\\) degrees higher this morning than it had been last night. His temperature this morning was \\(101.2\\) degrees. What was his temperature last night?<\/td>\n<td>58. The nurse reported that Tricia\u2019s daughter had gained \\(4.2\\) pounds since her last checkup and now weighs \\(31.6\\) pounds. How much did Tricia\u2019s daughter weigh at her last checkup?<\/td>\n<\/tr>\n<tr>\n<td>59. Ron\u2019s paycheck this week was \\(\\text{\\$17.43}\\) less than his paycheck last week. His paycheck this week was \\(\\text{\\$103.76}\\). How much was Ron\u2019s paycheck last week?<\/td>\n<td>60. Melissa\u2019s math book cost \\(\\text{\\$22.85}\\) less than her art book cost. Her math book cost \\(\\text{\\$93.75}\\). How much did her art book cost?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166482702466\" 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\">61.Construction<\/strong> Miguel wants to drill a hole for a \\(\\frac{5}{\\text{8}}\\phantom{\\rule{0.1em}{0ex}}\\text{-inch}\\) screw. The screw should be \\(\\frac{1}{12}\\) inch larger than the hole. Let \\(d\\) equal the size of the hole he should drill. Solve the equation \\(d+\\frac{1}{12}=\\frac{5}{8}\\) to see what size the hole should be.<\/td>\n<td><strong data-effect=\"bold\">Baking<\/strong>\u00a0 62. Kelsey needs \\(\\frac{2}{3}\\) cup of sugar for the cookie recipe she wants to make. She only has \\(\\frac{1}{4}\\) cup of sugar and will borrow the rest from her neighbour. Let \\(s\\) equal the amount of sugar she will borrow. Solve the equation \\(\\frac{1}{4}+s=\\frac{2}{3}\\) to find the amount of sugar she should ask to borrow.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166494586239\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>63. Write a word sentence that translates the equation \\(y-18=41\\) and then make up an application that uses this equation in its solution.<\/td>\n<td>64. Is \\(-18\\) a solution to the equation \\(3x=16-5x?\\) How do you know?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h1>Answers<\/h1>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>1. yes<\/td>\n<td>3. no<\/td>\n<td>5.<em data-effect=\"italics\"> x<\/em> = 5<\/td>\n<\/tr>\n<tr>\n<td>7. \\(b=\\frac{1}{2}\\)<\/td>\n<td>9.<em data-effect=\"italics\"> p<\/em> = \u221211.7<\/td>\n<td>11.<em data-effect=\"italics\"> a<\/em> = 10<\/td>\n<\/tr>\n<tr>\n<td>13. \\(x=\\frac{7}{3}\\)<\/td>\n<td>15.<em data-effect=\"italics\"> y<\/em> = 13.8<\/td>\n<td>17.<em data-effect=\"italics\"> x<\/em> = \u221227<\/td>\n<\/tr>\n<tr>\n<td>19. \\(q=-\\frac{1}{4}\\)<\/td>\n<td>21. 17<\/td>\n<td>23. 8<\/td>\n<\/tr>\n<tr>\n<td>25. \u221220<\/td>\n<td>27. 2<\/td>\n<td>29. \u22121.7<\/td>\n<\/tr>\n<tr>\n<td>31. \u22122<\/td>\n<td>33. \u22124<\/td>\n<td>35. 6<\/td>\n<\/tr>\n<tr>\n<td>37. \u221241<\/td>\n<td>39.<em data-effect=\"italics\"> x<\/em> + (\u22125) = 33; <em data-effect=\"italics\">x<\/em> = 38<\/td>\n<td>41.y \u2212 3 = \u221219; <em data-effect=\"italics\">y<\/em> = \u221216<\/td>\n<\/tr>\n<tr>\n<td>43.<em data-effect=\"italics\"> p<\/em> + 8 = 52; <em data-effect=\"italics\">p<\/em> = 44<\/td>\n<td>45. 5<em data-effect=\"italics\">c<\/em> \u2212 4<em data-effect=\"italics\">c<\/em> = 60; 60<\/td>\n<td>47. \\(f-\\frac{1}{3}=\\frac{1}{12};\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\)<\/td>\n<\/tr>\n<tr>\n<td>49. \u22129<em data-effect=\"italics\">m<\/em> + 10<em data-effect=\"italics\">m<\/em> = \u221225; <em data-effect=\"italics\">m<\/em> = \u221225<\/td>\n<td>51. Let <em data-effect=\"italics\">p<\/em> equal the number of pages read in the Psychology book 41 + <em data-effect=\"italics\">p<\/em> = 54. Jeff read pages in his Psychology book.<\/td>\n<td>53. Let <em data-effect=\"italics\">d<\/em> equal the daughter\u2019s age. d = 12 \u2212 5. Eva\u2019s daughter\u2019s age is 7 years old.<\/td>\n<\/tr>\n<tr>\n<td>55. 21 pounds<\/td>\n<td>57. 100.5 degrees<\/td>\n<td>59. \\$121.19<\/td>\n<\/tr>\n<tr>\n<td>61. \\(d=\\frac{13}{24}\\)<\/td>\n<td>63. 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 Using the Subtraction and Addition Properties of Equality\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.","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 equations using the Subtraction and Addition Properties of Equality<\/li>\n<li>Solve equations that need to be simplified<\/li>\n<li>Translate an equation and solve<\/li>\n<li>Translate and solve applications<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1166493765778\">We are now ready to \u201cget to the good stuff.\u201d You have the basics down and are ready to begin one of the most important topics in algebra: solving equations. The applications are limitless and extend to all careers and fields. Also, the skills and techniques you learn here will help improve your critical thinking and problem-solving skills. This is a great benefit of studying mathematics and will be useful in your life in ways you may not see right now.<\/p>\n<div id=\"fs-id1956457\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h1>\n<p id=\"fs-id1166497276639\">Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.<\/p>\n<div id=\"fs-id1329645\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Solution of an Equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/p>\n<\/div>\n<\/div>\n<p>The steps to determine if a value is a solution to an equation are listed here.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Determine whether a number is a solution to an equation.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-95\" class=\"stepwise\" type=\"1\">\n<li>Substitute the number for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting equation is true.\n<ul id=\"fs-id1703984\" data-bullet-style=\"bullet\">\n<li>If it is true, the number is a solution.<\/li>\n<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166492761655\" 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 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1518747\" data-type=\"problem\">\n<p id=\"fs-id1166484083630\">Determine whether <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3d805fa8462753e01e952ec103d999e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> is a solution for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-485cc73f0e9a4ebda0192946178961c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#43;&#51;&#61;&#56;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong><span style=\"font-size: 0.9em; word-spacing: normal;\">Solution<\/span><\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166491409809\" data-type=\"solution\">\n<table id=\"eip-id1168466426761\" class=\"unnumbered unstyled\" summary=\"The top line says 4y plus 3 equals 8y. Beside this is \u201cGiven.\u201d The next line says 4 times a red three-fourths plus 3 followed by an equal sign with a question mark, then 8 times a red three-fourths. Beside this is \u201cSubstitute three-fourths for y.\u201d Three-fourths is in red. The next line says 3 plus 3 equal sign with a question mark 6. Beside this is \u201cMultiply.\u201d The last line says 6 equals 6. Beside this is \u201cAdd. The solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468702694\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_01_001_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466078265\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><span id=\"eip-id1168469511022\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468288486\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-04-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1168468655391\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1877457\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3d805fa8462753e01e952ec103d999e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> results in a true equation, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-469181e98c8ec4b1bce8f57ea4ba4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> is a solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-485cc73f0e9a4ebda0192946178961c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#43;&#51;&#61;&#56;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/>.<\/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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1486889\" data-type=\"problem\">\n<p id=\"fs-id1951701\">Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d85ed4bb0138f3c213ad63cf5527e6d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> a solution for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b07ecffd8bdfd8e8551183a0c5852d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#43;&#50;&#61;&#54;&#121;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166497326966\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1603913\">no<\/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-id1698735\" data-type=\"problem\">\n<p id=\"fs-id1166484604448\">Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ebe787d6a6da051196dd63af46432e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> a solution for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c6b11e4f8ac1a95b97ff03d037a5b5eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#51;&#61;&#49;&#48;&#121;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166494755266\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166494591269\">no<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>In that section,we will model how the Subtraction and Addition Properties work and then we will apply them to solve equations.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1731715\" data-type=\"note\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>For all real numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"25\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-092c2c215b89a565a36b73ba234b32c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#99;&#61;&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"100\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Addition Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>For all real numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfaed44949cf9cfbeb3445de33aabd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"25\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb3e831fa117e5f6ffe14a23913c265e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#99;&#61;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1166497417158\">When you add or subtract the same quantity from both sides of an equation, you still have equality.<\/p>\n<\/div>\n<p id=\"eip-108\">We will introduce the <span class=\"no-emphasis\" data-type=\"term\">Subtraction Property of Equality<\/span>\u00a0by modeling equations with envelopes and counters. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_08_01_026\">(Figure .1)<\/a> models the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de8f79dc01c664efa0dfdb3ae6a7ec31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#51;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<div id=\"CNX_BMath_Figure_08_01_026\" class=\"bc-figure figure\">\n<figure style=\"width: 211px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_026-2.jpg\" alt=\"An envelope and three yellow counters are shown on the left side. On the right side are eight yellow counters.\" width=\"211\" height=\"129\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .1<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1856746\">The goal is to isolate the variable on one side of the equation. So we \u2018took away\u2019 <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;\" \/> from both sides of the equation and found the <span class=\"no-emphasis\" data-type=\"term\">solution<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1166490921090\">Some people picture a balance scale, as in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_08_01_001\">(Figure .2)<\/a>, when they solve equations.<\/p>\n<div id=\"CNX_BMath_Figure_08_01_001\" class=\"bc-figure figure\">\n<figure style=\"width: 476px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_001-2.jpg\" alt=\"Three balance scales are shown. The top scale has one red weight on each side and is balanced. Beside it is \u201c1 mass on each side equals balanced.\u201d The next scale has two weights on each side and is balanced. Beside it is \u201c2 masses on each side equals balanced.\u201d The bottom scale has one weight on the left and two on the right. The right side is lower than the left. Beside the image is \u201c1 mass on one side and 2 masses on the other equals unbalanced.\u201d\" width=\"476\" height=\"500\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .2<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1166497425012\">The quantities on both sides of the equal sign in an equation are equal, or balanced. Just as with the balance scale, whatever you do to one side of the equation you must also do to the other to keep it balanced.<\/p>\n<p id=\"fs-id1166491428047\">Let\u2019s see how to use Subtraction and Addition Properties of Equality to solve equations. We need to isolate the variable on one side of the equation. And we check our solutions by substituting the value into the equation to make sure we have a true statement.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1953663\" data-type=\"problem\">\n<p id=\"fs-id1736543\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87b53f4cd66ea4332e8e804d4b932cbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#49;&#49;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166488297178\" data-type=\"solution\">\n<p id=\"fs-id1487471\">To isolate <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;\" \/>, we undo the addition of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> by using the Subtraction Property of Equality.<\/p>\n<table id=\"eip-id1168468291100\" style=\"width: 100%;\" summary=\"The top line says x plus 11 equals negative 3. The next line says, \u201cSubtract 11 from each side, to 'undo' the addition.\u201d Beside this is x plus 11 minus a red 11 equals negative 3 minus a red 11. The next line says \u201csimplify.\u201d Beside this is x equals negative 14. The next line says \u201ccheck.\u201d Beside this is x plus 11 equals negative 3. The last line says \u201csubstitute\u201d and shows x equals negative 14, then a red negative 14 plus 11 followed by an equal sign with a question mark and a negative 3, then negative 3 equals negative 3 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168469834553\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Subtract 11 from each side to &#8220;undo&#8221; the addition.<\/td>\n<td><span id=\"eip-id1168466137434\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168466092262\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168466072125\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-04-2.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-78c2ca79114e6022ff05e53385758827_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466079144\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469869298\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_019_img-06-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1468740\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78c2ca79114e6022ff05e53385758827_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/> makes <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87b53f4cd66ea4332e8e804d4b932cbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#49;&#49;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\" \/> a true statement, we know that it is a solution to the equation.<\/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 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493722919\" data-type=\"problem\">\n<p id=\"fs-id900542\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7682d57df5ce236f50bf227b84a875a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#57;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166492788206\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497163046\"><em data-effect=\"italics\">x<\/em> = \u221216<\/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-id1944892\" data-type=\"problem\">\n<p id=\"fs-id1166491429192\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38a9a34f1505346750ddc065325697aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#49;&#54;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166493761190\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491084479\"><em data-effect=\"italics\">x<\/em> = \u221220<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166490870130\">In the original equation in the previous example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> was added to 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;\" \/>, so we subtracted <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> to \u2018undo\u2019 the addition. In the next example, we will need to \u2018undo\u2019 subtraction by using the <span class=\"no-emphasis\" data-type=\"term\">Addition Property of Equality<\/span>.<\/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-id1166479028976\" data-type=\"problem\">\n<p id=\"fs-id1511517\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ef7949f196302ce8493fe00ee348113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#45;&#52;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"92\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166478988064\" data-type=\"solution\">\n<table id=\"eip-id1168467157298\" style=\"width: 100%;\" summary=\"The first line says m minus 4 equals negative 5. The next line says, \u201cAdd 4 to each side, to 'undo' the subtraction.\u201d Beside this is m minus 4 plus a red 4 equals negative 5 plus a red 4. The next line says \u201csimplify\u201d and shows m equals negative 1. The following line says to \u201ccheck\u201d and shows m minus 4 equals negative 5. Below this is \u201csubstitute\u201d and m equals negative 1. Below that is a red negative 1 minus 4 followed by an equal sign with a question mark and negative 5. The last line shows negative 5 equals negative 5 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468473383\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add 4 to each side to &#8220;undo&#8221; the subtraction.<\/td>\n<td><span id=\"eip-id1168467340413\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-02-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td><span id=\"eip-id1168467332056\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-03-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468552729\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-04-2.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-ec3d084a8add5b00b06df1310c62281e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468614495\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-05-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467261089\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_020_img-06-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>The solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ef7949f196302ce8493fe00ee348113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#45;&#52;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"92\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec3d084a8add5b00b06df1310c62281e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/>.<\/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-id1508126\" data-type=\"problem\">\n<p id=\"fs-id1166493484246\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fd57f7be90b0f1b88a7d7b2e8d94ce3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#54;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491411267\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490916413\">\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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491003339\" data-type=\"problem\">\n<p id=\"fs-id1166491256493\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46370d5685dabc90b78db03b53aa54c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#53;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"87\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1485263\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1482600\">\u22124<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1486893\">Now let\u2019s\u00a0 solve equations with fractions.<\/p>\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 data-type=\"problem\">\n<p id=\"fs-id1806883\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-618c865de3eff7741540b704c170dea1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"76\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166494770805\" data-type=\"solution\">\n<table id=\"eip-id1168468255179\" style=\"width: 100%;\" summary=\"The first line says n minus 3 eighths equals one half. The next line says, \u201cUse the Addition Property of Equality.\u201d Beside this is n minus 3 over 8 plus a red 3 over 8 equals one half plus a red 3 over 8. The next line says \u201cFind the LCD to add the fractions on the right.\u201d Beside that is n minus 3 over 8 plus 3 over 8 equals 4 over 8 plus 3 over 8. The next line says \u201csimplify\u201d and shows n equals 7 over 8. Below that is \u201ccheck\u201d and n minus 3 eighths equals one half. The following line says to substitute n equals 7 over 8 and shows a red 7 over 8 minus 3 over 8 followed by an equal sign with a question mark and one half. The next line says \u201csubtract\u201d and shows 4 over 8, equal sign with a question mark, 1 half. The last line says \u201csimplify\u201d and says one half equals one half with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168466176178\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-01-2.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168469603754\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Find the LCD to add the fractions on the right.<\/td>\n<td><span id=\"eip-id1168469611733\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify<\/td>\n<td><span id=\"eip-id1168469683726\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168466175504\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468241254\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><span id=\"eip-id1168467114144\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168469872572\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469615789\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_021_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/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-id2050763\" data-type=\"problem\">\n<p id=\"fs-id1430998\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-343ff08595a25378e5f2533e3145ea3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1455960\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491425616\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b07593bb06e86cfd8aa5be2606ff78c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166493722928\" data-type=\"problem\">\n<p id=\"fs-id1449225\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-602e71ff8d8889287401657ec646a633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1798095\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1766639\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d535ac25e39c2307a1afc2e8c63e757e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166482443040\">Let&#8217;s solve equations that contained decimals.<\/p>\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-id1166497408110\" data-type=\"problem\">\n<p id=\"fs-id1166490790049\">Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4836f53439906ab4bacc2c97da21b8a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#51;&#46;&#55;&#61;&#52;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"100\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1736242\" data-type=\"solution\">\n<table id=\"eip-id1168468751492\" style=\"width: 100%;\" summary=\"The top line says a minus 3.7 equals 4.3. The next line says \u201cUse the Addition Property of Equality.\u201d Beside that is a minus 3.7 plus a red 3.7 equals 4.3 plus a red 3.7. The next line says to add and shows a equals 8. The next line says to check and shows a minus 3.7 equals 4.3. Below that is \u201cSubstitute a equals 8\u201d and a red 8 minus 3.7 followed by an equal sign with a question mark and 4.3. The last line says to simplify and shows 4.3 equals 4.3 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168467170715\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168468232824\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add.<\/td>\n<td><span id=\"eip-id1168468412922\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><span id=\"eip-id1168468389351\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-04-1.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-e745fe99e971c118c9139d6d1fd17c94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168465145363\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468520006\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_022_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/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-id1357810\" data-type=\"problem\">\n<p id=\"fs-id1166492771569\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffa83b72c20b34f8102913d2812e78f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#45;&#50;&#46;&#56;&#61;&#51;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"99\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166484109037\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">b<\/em> = 6.4<\/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 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1768687\" data-type=\"problem\">\n<p id=\"fs-id1249306\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23240cdbc0600b697dae9ecfd5f775f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#45;&#54;&#46;&#57;&#61;&#55;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"98\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1418529\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">c<\/em> = 14<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations That Need to Be Simplified<\/h1>\n<\/div>\n<div id=\"fs-id1471572\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166494591280\">In the examples up to this point, we have been able to isolate the variable with just one operation. Many of the equations we encounter in algebra will take more steps to solve. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality. You should always simplify as much as possible before trying to isolate the variable.<\/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-id1693654\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e114370eaefa71d10f73b70b0b75b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#55;&#45;&#50;&#120;&#45;&#52;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"152\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1475828\" data-type=\"solution\">\n<p id=\"fs-id1495618\">The left side of the equation has an expression that we should simplify before trying to isolate the variable.<\/p>\n<table id=\"eip-id1168467171254\" style=\"height: 286px; width: 100%;\" summary=\"The first line shows the equation 3x minus 7 minus 2x minus 4 equals 1. The next line says, \u201cRearrange the terms, using the Commutative Property of Addition.\u201d Beside this is 3x minus 2x minus 7 minus 4 equals 1. The next line says, \u201cCombine like terms.\u201d Beside this is x minus 11 equals 1. The next line says, \u201cAdd 11 to both sides to isolate x.\u201d Beside this is x minus 11 plus a red 11 equals 1 plus a red 11. The last line says \u201csimplify\u201d and shows x equals 12.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px; width: 411.25px;\"><\/td>\n<td style=\"height: 24px; width: 198.75px;\"><span id=\"eip-id1168468454842\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 411.25px;\">Rearrange the terms, using the Commutative Property of Addition.<\/td>\n<td style=\"height: 22px; width: 198.75px;\"><span id=\"eip-id1168468592120\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 411.25px;\">Combine like terms.<\/td>\n<td style=\"height: 23px; width: 198.75px;\"><span id=\"eip-id1168468458434\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 411.25px;\">Add 11 to both sides to isolate <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 style=\"height: 23px; width: 198.75px;\"><span id=\"eip-id1168467375475\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 411.25px;\">Simplify.<\/td>\n<td style=\"height: 22px; width: 198.75px;\"><span id=\"eip-id1168468451956\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_010_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 172px;\">\n<td style=\"height: 172px; width: 411.25px;\">Check.<br \/>\nSubstitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d28a9fa084bc02bc048b780624acf003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: -1px;\" \/> into the original equation.<br \/>\n<span id=\"fs-id1480549\" data-type=\"media\" data-alt=\"The top line shows 3x minus 7 minus 2x minus 4 equals 1. Below this is 3 times a red 12 minus 7 minus 2 times a red 12 minus 4 equals 1. Next is 36 minus 7 minus 24 minus 4 equals 1. Below is 29 minus 24 minus 4 equals 1. Next is 5 minus 4 equals 1. Last is 1 equals 1.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_011_img-1.jpg\" alt=\"The top line shows 3x minus 7 minus 2x minus 4 equals 1. Below this is 3 times a red 12 minus 7 minus 2 times a red 12 minus 4 equals 1. Next is 36 minus 7 minus 24 minus 4 equals 1. Below is 29 minus 24 minus 4 equals 1. Next is 5 minus 4 equals 1. Last is 1 equals 1.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"height: 172px; width: 198.75px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1303501\">The solution checks.<\/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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1241927\" data-type=\"problem\">\n<p id=\"fs-id1731867\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e36bc2e05f7a52aa23c0d874d7ef268c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#45;&#52;&#45;&#55;&#121;&#45;&#55;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1502572\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166476201528\"><em data-effect=\"italics\">y<\/em> = 15<\/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-id1733102\" data-type=\"problem\">\n<p id=\"fs-id1437081\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3622e6fd9861a427690b44bede608ac0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#122;&#43;&#53;&#45;&#53;&#122;&#45;&#52;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"151\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1357223\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491297361\"><em data-effect=\"italics\">z<\/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 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547337\" data-type=\"problem\">\n<p id=\"fs-id1166497425790\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19e5cfadd1d148bc80a3e148fdbdd684_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#110;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492887596\" data-type=\"solution\">\n<p id=\"fs-id1302362\">The left side of the equation has an expression that we should simplify.<\/p>\n<table id=\"eip-id1168468254328\" style=\"width: 100%;\" summary=\"The top line says \u201cgiven\u201d and shows 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says \u201cdistribute on the left\u201d and shows 3n minus 12 minus 2n equals negative 3. The next line says, \u201cUse the Commutative Property to rearrange terms.\u201d Beside this is 3n minus 2n minus 12 equals negative 3. The next step says \u201cCombine like terms.\u201d Beside this is n minus 12 equals negative 3. The next line says, \u201cIsolate n using the Addition Property of Equality.\u201d Beside this is n minus 12 plus a red 12 equals negative 3 plus a red 12. The last line says \u201csimplify\u201d and shows n equals 9.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468249958\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute on the left.<\/td>\n<td><span id=\"eip-id1168468557711\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange terms.<\/td>\n<td><span id=\"eip-id1168467473331\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168467453602\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Isolate <em data-effect=\"italics\">n<\/em> using the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168468554542\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_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-id1168468358150\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_012_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<br \/>\nSubstitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd7d88ae080606b45d7242624deeb556_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> into the original equation.<br \/>\n<span id=\"fs-id1494005\" data-type=\"media\" data-alt=\"The top line says 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says 3 times parentheses red 9 minus 3 minus 2 times red 9 equals negative 3. The next line says 3 times 5 minus 18 equals negative 3. Below this is 15 minus 18 equals negative 3. Last is negative 3 equals negative 3.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_013_img-1.jpg\" alt=\"The top line says 3 times parentheses n minus 4 minus 2n equals negative 3. The next line says 3 times parentheses red 9 minus 3 minus 2 times red 9 equals negative 3. The next line says 3 times 5 minus 18 equals negative 3. Below this is 15 minus 18 equals negative 3. Last is negative 3 equals negative 3.\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\nThe solution checks.<\/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 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491296425\" data-type=\"problem\">\n<p id=\"fs-id834398\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e267a99a7ecec78ac5880289ddf459a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#112;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1444663\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">p<\/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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166498049515\" data-type=\"problem\">\n<p id=\"fs-id1242285\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-805865e631743a889f7b28de68808315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;&#113;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491403679\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1491162\"><em data-effect=\"italics\">q<\/em> = \u221216<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id834918\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166484082143\" data-type=\"exercise\">\n<div id=\"fs-id1166491296425\" 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-id1166493761721\" data-type=\"problem\">\n<p id=\"fs-id1724676\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4daca5fa7de01fe323e08249f66a01aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#107;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#107;&#61;&#45;&#50;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"192\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166483694459\" data-type=\"solution\">\n<p>Both sides of the equation have expressions that we should simplify before we isolate the variable.<\/p>\n<table id=\"eip-id1168469785088\" style=\"width: 100%;\" summary=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. The next line says \u201cDistribute on the left, subtract on the right.\u201d Beside that is 6k minus 2 minus 5k equals negative 9. The next line says \u201cUse the Commutative Property of Addition.\u201d Beside that is 6k minus 5k minus 2 equals negative 9. The next step says \u201ccombine like terms\u201d and shows k minus 2 equals negative 9. The next step says, \u201cUndo subtraction by using the Addition Property of Equality.\u201d Beside that is k minus 2 plus a red 2 equals negative 9 plus a red 2. The last step says to simplify and shows k equals negative 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466140979\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute on the left, subtract on the right.<\/td>\n<td><span id=\"eip-id1168469711596\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property of Addition.<\/td>\n<td><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469577466\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Undo subtraction by using the Addition Property of Equality.<\/td>\n<td><span id=\"eip-id1168469699676\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_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-id1168466203200\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_023_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-1b3160c0de6b3240ef095dbb594134a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466203200\" data-type=\"media\" data-alt=\".\"><span data-type=\"media\" data-alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_014_img-1.jpg\" alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><span id=\"eip-id1168466203200\" data-type=\"media\" data-alt=\".\"><span data-type=\"media\" data-alt=\"The top line says 2 times parentheses 3k minus 1 minus 5k equals negative 2 minus 7. Below this is 2 times parentheses red negative 7 minus 1 minus 5 times red negative 7 equals negative 2 minus 7. The next line says 2 times parentheses negative 21 minus 1 minus 5 times negative 7 equals negative 9. Below that is 2 times negative 22 plus 35 equals negative 9. Next is negative 44 plus 35 equals negative 9. The last line says negative 9 equals negative 9.\">\u00a0<\/span><\/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 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1317627\" data-type=\"exercise\">\n<div id=\"fs-id1457105\" data-type=\"problem\">\n<p id=\"fs-id1877708\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21d7d5c0923b6e656e1bf952d79a4ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#104;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#104;&#61;&#45;&#54;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1388025\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1500361\"><em data-effect=\"italics\">h<\/em> = \u22121<\/p>\n<\/details>\n<\/div>\n<\/div>\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-id1496617\" data-type=\"problem\">\n<p id=\"fs-id1166494737777\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cfc59567abf34df3a0de900972645d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;&#120;&#61;&#45;&#50;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1956094\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1526415\"><em data-effect=\"italics\">x<\/em> = 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate an Equation and Solve<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1580769\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166488299698\">Previously, we translated word sentences into equations. The first step is to look for the word (or words) that translate(s) to the equal sign. The list below reminds us of some of the words that translate to the equal sign (=):<\/p>\n<ul>\n<li>is<\/li>\n<li>is equal to<\/li>\n<li>is the same as<\/li>\n<li>the result is<\/li>\n<li>gives<\/li>\n<li>was<\/li>\n<li>will be<\/li>\n<\/ul>\n<p>Let\u2019s review the steps we used to translate a sentence into an equation.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Translate a word sentence to an algebraic equation.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-112\" class=\"stepwise\" type=\"1\">\n<li>Locate the &#8220;equals&#8221; word(s). Translate to an equal sign.<\/li>\n<li>Translate the words to the left of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<li>Translate the words to the right of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1314958\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<p>Now we are ready to try an example.<\/p>\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-id1166491761371\" data-type=\"problem\">\n<p>Translate and solve: five more than <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 equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc1c5ee273f78a117868c9594082c74b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"eip-id1168466284401\" style=\"width: 100%;\" summary=\"The first line says \u201cFive more than x is equal to 26.\u201d The next line says \u201ctranslate\u201d and shows x plus 5 equals 26. The next line says \u201csubtract 5 from both sides,\u201d and shows x plus 5 minus a red 5 equals 26 minus a red 5. The next line says to simplify and shows x equals 21. The last step says \u201cCheck. Is 26 five more than 21?\u201d Below that is 21 plus 5, equal sign with a question mark, 26. Then, 26 equals 26 and a check mark. Below that, \u201cThe solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168466049464\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides.<\/td>\n<td><span id=\"eip-id1168469761474\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_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-id1168469866749\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc1c5ee273f78a117868c9594082c74b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> five more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>?<\/td>\n<td><span id=\"eip-id1168466312585\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469622050\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\nThe solution checks.<\/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-id1166476201092\" data-type=\"problem\">\n<p id=\"fs-id1491170\">Translate and solve: Eleven more than <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 equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20bf590fc81a78a705705c8aad69df9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166498082806\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1505239\"><em data-effect=\"italics\">x<\/em> + 11 = 41; <em data-effect=\"italics\">x<\/em> = 30<\/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-id1508494\" data-type=\"problem\">\n<p id=\"fs-id1166494584879\">Translate and solve: Twelve less than <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 equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-deb4bebaec9fe47ccd035848be13a879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1526438\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1335207\"><em data-effect=\"italics\">y<\/em> \u2212 12 = 51; <em data-effect=\"italics\">y<\/em> = 63<\/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 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547575\" data-type=\"problem\">\n<p id=\"fs-id1166483685755\">Translate and solve: The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7e091e8564d41f9146826b36634901e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fd3856fcad97dc6a0c30c08faeab2c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1768035\" data-type=\"solution\">\n<table id=\"eip-id1168468483860\" style=\"width: 100%;\" summary=\"The first line says \u201cThe top line says \u201cTranslate.\u201d Beside that is \u201cThe difference of 5p and 4p is 23.\u201d Below \u201cthe difference of 5p and 4p\u201d is 5p minus 4p. Below \u201cis\u201d is an equal sign. Below 23 is 23. The next line says \u201csimplify\u201d and says p equals 23. The next line says \u201ccheck\u201d and shows 5p minus 4p equals 23. Below that is 5 times 23 minus 4 times 23 equal sign with a question mark 23. The next line says 23 times parentheses 5 minus 4 equal sign with a question mark 23. The next line says 23 times 1 equal sign with a question mark 23. The last line shows 23 equals 23 and says \u201cThe solution checks.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168466163340\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466233449\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<br \/>\n<span id=\"eip-id1168469741227\" data-type=\"media\" data-alt=\".\"><\/span><\/td>\n<td><span id=\"eip-id1168469511332\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168466231412\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469873016\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469741227\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id830325\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1365772\" data-type=\"exercise\">\n<div id=\"fs-id1526438\" data-type=\"solution\">\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-id1166479044245\" data-type=\"problem\">\n<p id=\"fs-id1456338\">Translate and solve: The difference of <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;\" \/> and <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;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1456603\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1479670\">4<em data-effect=\"italics\">x<\/em> \u2212 3<em data-effect=\"italics\">x<\/em> = 14; <em data-effect=\"italics\">x<\/em> = 14<\/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-id1538802\" data-type=\"problem\">\n<p id=\"fs-id847862\">Translate and solve: The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57444a17a512a6be97a4dfabc5c69f84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a79e1b033cc92ebc730ed43c5dc6497e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> is <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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1494370\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1484361\">7<em data-effect=\"italics\">a<\/em> \u2212 6<em data-effect=\"italics\">a<\/em> = \u22128; <em data-effect=\"italics\">a<\/em> = \u22128<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1454996\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Translate and Solve Applications<\/h1>\n<p id=\"fs-id1166491265463\">In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We\u2019ll start by restating the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.<\/p>\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-id1542722\" data-type=\"problem\">\n<p id=\"fs-id1166491402029\">The Robles family has two dogs, Buster and Chandler. Together, they weigh <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02f9323038ee8eec0414eae81aa8e8a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> pounds.<\/p>\n<p id=\"fs-id1505848\">Chandler weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80588c2af70b499bde2614a130c98b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> pounds. How much does Buster weigh?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1487807\" data-type=\"solution\">\n<table id=\"eip-id1168468537406\" class=\"unnumbered unstyled\" style=\"width: 471px; height: 238px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">Read the problem carefully.<\/td>\n<td style=\"width: 269.406px; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Identify what you are asked to find, and choose a variable to represent it.<\/td>\n<td style=\"width: 269.406px; height: 30px;\">How much does Buster weigh?<br \/>\nLet <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b47726c83ea776f14901caa5826ff7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/> Buster&#8217;s weight<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">Write a sentence that gives the information to find it.<\/td>\n<td style=\"width: 269.406px; height: 14px;\">Buster&#8217;s weight plus Chandler&#8217;s weight equals 71 pounds.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\">We will restate the problem, and then include the given information.<\/td>\n<td style=\"width: 269.406px; height: 14px;\">Buster&#8217;s weight plus 28 equals 71.<\/td>\n<\/tr>\n<tr style=\"height: 29px;\">\n<td style=\"width: 171.406px; height: 29px;\">Translate the sentence into an equation, using the variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 269.406px; height: 29px;\"><span id=\"eip-id1168468704181\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 49px;\">\n<td style=\"width: 171.406px; height: 49px;\" data-valign=\"top\">Solve the equation using good algebraic techniques.<\/td>\n<td style=\"width: 269.406px; height: 49px;\"><span id=\"eip-id1168467446215\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168467446225\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Check the answer in the problem and make sure it makes sense.<\/td>\n<td style=\"width: 269.406px; height: 30px;\">Is 43 pounds a reasonable weight for a dog? Yes. Does Buster&#8217;s weight plus Chandler&#8217;s weight equal 71 pounds?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\"><\/td>\n<td style=\"width: 269.406px; height: 14px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fb3bdb1b8404d69da9475589fc2ba56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#51;&#43;&#50;&#56;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#55;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 171.406px; height: 14px;\" data-align=\"center\"><\/td>\n<td style=\"width: 269.406px; height: 14px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a53e7e09a7e5eceee83f9da030f80c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#49;&#61;&#55;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 171.406px; height: 30px;\">Write a complete sentence that answers the question, &#8220;How much does Buster weigh?&#8221;<\/td>\n<td style=\"width: 269.406px; height: 30px;\">Buster weighs 43 pounds<\/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-id1166493492477\" data-type=\"problem\">\n<p id=\"fs-id1166479044410\">Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> pounds. Zeus weighs <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;\" \/> pounds. How much does Athena weigh?<\/p>\n<\/div>\n<div id=\"fs-id1508911\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1788943\"><em data-effect=\"italics\">a<\/em> + 6 = 13; Athena weighs 7 pounds.<\/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 id=\"fs-id1877445\" data-type=\"problem\">\n<p id=\"fs-id1342552\">Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e3b92253edc96beb52811ed30fc440d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> books. Sam has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc1c5ee273f78a117868c9594082c74b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> books. How many books does Henry have?<\/p>\n<\/div>\n<div id=\"fs-id1691302\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497212257\">26 + <em data-effect=\"italics\">h<\/em> = 68; Henry has 42 books.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Devise a Problem-Solving Strategy<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168469608282\" class=\"stepwise\" type=\"1\">\n<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n<li>Identify what you are looking for.<\/li>\n<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1500299\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166492772961\" data-type=\"exercise\">\n<div id=\"fs-id1166493492477\" data-type=\"problem\">\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-id1555567\" data-type=\"problem\">\n<p id=\"fs-id1505680\">Shayla paid <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c76882df5906b1bbadd100d53a6e584_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#50;&#52;&#44;&#53;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -4px;\" \/> for her new car. This was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976109fa27f300e3abe16e76e72d70d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#56;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"35\" style=\"vertical-align: -1px;\" \/> less than the sticker price. What was the sticker price of the car?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492477793\" data-type=\"solution\">\n<table id=\"eip-id1168469715820\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>&#8220;What was the sticker price of the car?&#8221;<\/td>\n<\/tr>\n<tr>\n<td>Assign a variable.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12ac9f5dee0c0d9acdb247ec52211d05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"26\" style=\"vertical-align: 0px;\" \/> the sticker price of the car.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>&#36;24,575 is &#36;875 less than the sticker price<br \/>\n&#36;24,575 is &#36;875 less than <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;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><span id=\"eip-id1168469875413\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve.<\/td>\n<td><span id=\"eip-id1168469781730\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469577361\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_01_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>Is &#36;875 less than &#36;25,450 equal to &#36;24,575?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70c0ef5e621e0919b4c7c6c0d951180f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#44;&#52;&#53;&#48;&#45;&#56;&#55;&#53;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#50;&#52;&#44;&#53;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"176\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b6900a26c5d8b6d6f3c0a59793bdb43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#44;&#53;&#55;&#53;&#61;&#50;&#52;&#44;&#53;&#55;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -4px;\" \/>\u2713<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that answers the question.<\/td>\n<td>The sticker price was &#36;25,450.<\/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 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166478995641\" data-type=\"problem\">\n<p id=\"fs-id1166497147158\">Translate into an algebraic equation and solve: Eddie paid <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14795ce94e1a3bd1b06396bc9f5b7950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#57;&#44;&#56;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -4px;\" \/> for his new car. This was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20546c3344c0223aa7de9eab482a37ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#44;&#48;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"49\" style=\"vertical-align: -4px;\" \/> less than the sticker price. What was the sticker price of the car?<\/p>\n<\/div>\n<div id=\"fs-id1166497360359\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1416179\">19,875 = <em data-effect=\"italics\">s<\/em> \u2212 1025; the sticker price is &#36;20,900.<\/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 id=\"fs-id1166492076305\" data-type=\"problem\">\n<p id=\"fs-id1514129\">Translate into an algebraic equation and solve: The admission price for the movies during the day is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e49a6f588c110ee367a9f4f18ec604b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#55;&#46;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/>. This is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f6e07841a146dae959569e14d603928_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#51;&#46;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> less than the price at night. How much does the movie cost at night?<\/p>\n<\/div>\n<div id=\"fs-id1511804\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>7.75 = <em data-effect=\"italics\">n<\/em> \u2212 3.25; the price at night is &#36;11.00.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1443773\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1233682\" data-type=\"exercise\">\n<div id=\"fs-id1166478995641\" data-type=\"problem\">\n<ul id=\"eip-937\">\n<li><strong>Determine whether a number is a solution to an equation.<\/strong>\n<ol id=\"eip-id1170325336254\" class=\"stepwise\" type=\"1\">\n<li>Substitute the number for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting equation is true.<\/li>\n<\/ol>\n<p>If it is true, the number is a solution.<br \/>\nIf it is not true, the number is not a solution.<\/li>\n<li><strong>Subtraction and Addition Properties of Equality<\/strong>\n<ul id=\"eip-id1170322764024\">\n<li><strong>Subtraction Property of Equality<\/strong><br \/>\nFor all real numbers <em data-effect=\"italics\">a, b,<\/em> and <em data-effect=\"italics\">c<\/em>,<br \/>\nif <em data-effect=\"italics\">a = b<\/em> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-092c2c215b89a565a36b73ba234b32c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#99;&#61;&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"100\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li><strong>Addition Property of Equality<\/strong><br \/>\nFor all real numbers <em data-effect=\"italics\">a, b,<\/em> and <em data-effect=\"italics\">c<\/em>,<br \/>\nif <em data-effect=\"italics\">a = b<\/em> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb3e831fa117e5f6ffe14a23913c265e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#99;&#61;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Translate a word sentence to an algebraic equation.<\/strong>\n<ol id=\"eip-id1170324011027\" class=\"stepwise\" type=\"1\">\n<li>Locate the \u201cequals\u201d word(s). Translate to an equal sign.<\/li>\n<li>Translate the words to the left of the \u201cequals\u201d word(s) into an algebraic expression.<\/li>\n<li>Translate the words to the right of the \u201cequals\u201d word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Problem-solving strategy<\/strong>\n<ol id=\"eip-id1170325411872\" class=\"stepwise\" type=\"1\">\n<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n<li>Identify what you are looking for.<\/li>\n<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1170326208984\">\n<dt>solution of an equation<\/dt>\n<dd id=\"fs-id1170323908665\">A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<div id=\"fs-id1946531\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1495611\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h2>\n<p id=\"eip-551\">In the following exercises, determine whether the given value is a solution to the equation.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>1. Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d1b0ab367be28c3198c1ffa9c6a6c76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d53161f2a699ac829df4ce6f8170a8a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#43;&#50;&#61;&#49;&#48;&#121;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>2. Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c079d7a942761124394a871098a2020e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48894eccb0845e510ed6bff81e089c26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#51;&#61;&#57;&#120;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>3. Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06fa5bef24cb67d936d55c3027f6ed42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3ea79393ed812c1d53750f55a4e68cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#117;&#45;&#49;&#61;&#54;&#117;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"100\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>4. Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d5a78b569a6e33a5191ad7747ba2e6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#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;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92b3c6de18ffb17df1ea29cd2904a78f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#118;&#45;&#50;&#61;&#51;&#118;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"98\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1770916\">In the following exercises, solve each equation.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a868e10ecc74f91305dc1469f14fceb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c62eba716075ea60998f9c5a9558d025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#53;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50b3f1347e30336afed86e9bede3984d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"73\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c92180b6a8a73fde97bdf05b78d50c45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c5a7efd37629922e6445880b98891a76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#43;&#50;&#46;&#52;&#61;&#45;&#57;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8d04dba84a2e912114d6ffd2c88e6b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#43;&#55;&#46;&#57;&#61;&#49;&#49;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5581f49eb81963767960edcfb4925d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#51;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f666a330c75aa502ead3aa1979eadc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#45;&#56;&#61;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"102\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-865fcfe43dde968558a5d4b8f70dc0cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ca45874938b60b801381baa649f02e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77b821bb979aa8ff0c70cde91c60006d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#51;&#46;&#56;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b191a7de0668df368c8527271727ee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#55;&#46;&#50;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4b264fb83406258e0236d34b3b58280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#49;&#53;&#61;&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1f0efbc6dc6471a976b4e251e615a63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#43;&#53;&#46;&#50;&#61;&#45;&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"113\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-659ed02d05d144180f1fbfce0479b19b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a9a865c36bab680b8de14e7e60a88a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1944060\">Solve Equations that Need to be Simplified<\/h2>\n<p id=\"eip-244\">In the following exercises, solve each equation.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eeee3165cf1590a9b445c8d725b343db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#43;&#54;&#45;&#56;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"117\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dd30d7da1465673799f36925ed003f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#43;&#51;&#45;&#49;&#48;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d425cd7c9356e6783836b2f67dab82e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#56;&#45;&#53;&#120;&#43;&#49;&#54;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"170\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4c78c5ba137ef1bb4f9c87c510a4409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#43;&#53;&#45;&#56;&#120;&#43;&#49;&#52;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"171\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51aae71d521a52a6c75afdab91b3ed04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#110;&#45;&#49;&#55;&#43;&#57;&#110;&#45;&#52;&#61;&#45;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"198\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2305b5a0db1e0fc9734463001178dc92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#120;&#45;&#49;&#49;&#43;&#55;&#120;&#45;&#53;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"198\" 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-762d3578c7bf49ca1ef74779a104cd7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e82f2e9216167cc63d5d510278f59c22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#121;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-315f7119c59e3cb6bd0ebedb69f1461c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#50;&#46;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#119;&#61;&#57;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a2275dd024bee09ab64e95994d50b8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#49;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#117;&#61;&#52;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" 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-ece1854c5fbd9d280b1395fcb2691011_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;&#120;&#61;&#45;&#51;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-246f1eae2f1281619cacd18908da869c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;&#121;&#61;&#45;&#55;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"195\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf7fb115a2ff37a42a2190946e4ba964_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#53;&#109;&#45;&#52;&#61;&#51;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"228\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-195208ed8482caa584479647afdde1e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#52;&#110;&#43;&#57;&#61;&#49;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"218\" 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-f16be02e21814580337733da9377e80a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#107;&#43;&#56;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be5f37d02ec8b1fe846a4b8f426a63ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#106;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#106;&#45;&#49;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"169\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5deb16c1f7f81e4209d54889b3612fd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#99;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"188\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c7e91ec54ede4ad34b5a8b6b9f2bce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#97;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id679510\">Translate to an Equation and Solve<\/h2>\n<p id=\"eip-947\">In the following exercises, translate to an equation and then solve.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>39. The sum of <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;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d60b54f293e27e5e622846ba8e485376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>40.Five more than <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 equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>41.Three less than <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 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e22bf27371ae8e82f2cf9857cc59c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td>42. Ten less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4066673cb5834f8ce47cc6896c29963a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>43. Eight more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30352d66e4a511eedaaaf1c7497a30c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>44. The sum of <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;\" \/> and <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;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-89bc2c119dcafc9b555c6b2841530d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>45. The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-422359d3218bbdfb79ae263f7f9b88b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9af1c5edef018512e7abd86e6b9bd21b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7029ea134aa43ac5ffd9f780e196307d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>46. The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4dc36d20a7690e84c99b1c91d651a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2e766fef3082260b54b584383d424b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>47. The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34f0e870957984f6c69249b8cf4f5813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e697137c2fc49524ec52982e9a9dc34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td>48. The difference 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;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c27e6c52f9cb0bf70516c13f69448e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> is <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;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>49. The sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-130a5732c65a73a5c3773f2d6f51b012_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"37\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba09b44012812da3964cb4c05f16a3e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-170b493658855d7211748be1a7029d86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>50. The sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56fa39fe2da04e8588de19e0ca427d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"33\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e666400939039516208079bc6ec659b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"20\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce2979511e6a27a1bd61ca970c655b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166488297752\">Translate and Solve Applications<\/h2>\n<p>In the following exercises, translate into an equation and solve.<\/p>\n<table>\n<tbody>\n<tr>\n<td>51.Jeff read a total of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66ceeedc341151a1adecf7dd22c17553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -1px;\" \/> pages in his English and Psychology textbooks. He read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20bf590fc81a78a705705c8aad69df9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> pages in his English textbook. How many pages did he read in his Psychology textbook?<\/td>\n<td>52. Pilar drove from home to school and then to her aunt\u2019s house, a total of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> miles. The distance from Pilar\u2019s house to school is <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;\" \/> miles. What is the distance from school to her aunt\u2019s house?<\/td>\n<\/tr>\n<tr>\n<td>53. Eva\u2019s daughter is <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;\" \/> years younger than her son. Eva\u2019s son is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> years old. How old is her daughter?<\/td>\n<td>54. Pablo\u2019s father is <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;\" \/> years older than his mother. Pablo\u2019s mother is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-663d228316bfd115aace82901fc82ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> years old. How old is his father?<\/td>\n<\/tr>\n<tr>\n<td>55. For a family birthday dinner, Celeste bought a turkey that weighed <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;\" \/> pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> pounds. How much did the Thanksgiving turkey weigh?<\/td>\n<td>56. Allie weighs <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;\" \/> pounds less than her twin sister Lorrie. Allie weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0763ae919089a8912670c5eb26c45969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> pounds. How much does Lorrie weigh?<\/td>\n<\/tr>\n<tr>\n<td>57. Connor\u2019s temperature was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce05b6a62893de03d6e74ce9452fa4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> degrees higher this morning than it had been last night. His temperature this morning was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd6f839654a7837564a284923915f1d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#49;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: -1px;\" \/> degrees. What was his temperature last night?<\/td>\n<td>58. The nurse reported that Tricia\u2019s daughter had gained <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b51aa9707a66a85997f31501edc50c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> pounds since her last checkup and now weighs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85a0dcd0db8eaf8893c83b82f8033cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#49;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> pounds. How much did Tricia\u2019s daughter weigh at her last checkup?<\/td>\n<\/tr>\n<tr>\n<td>59. Ron\u2019s paycheck this week was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad9bcfaedadd13f09d266621d50d5d1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#55;&#46;&#52;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -1px;\" \/> less than his paycheck last week. His paycheck this week was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aec4af4bb04f1497d0ed3fa583104c4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#48;&#51;&#46;&#55;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -1px;\" \/>. How much was Ron\u2019s paycheck last week?<\/td>\n<td>60. Melissa\u2019s math book cost <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9129fb6ea643977bb773066ad65d5f17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#50;&#50;&#46;&#56;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/> less than her art book cost. Her math book cost <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2a1eaace838723ee474326f4ba2054_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#57;&#51;&#46;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/>. How much did her art book cost?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166482702466\" 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\">61.Construction<\/strong> Miguel wants to drill a hole for a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-09e5ddfbc095bb3eb44838c304109a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#125;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#105;&#110;&#99;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/> screw. The screw should be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e697137c2fc49524ec52982e9a9dc34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -7px;\" \/> inch larger than the hole. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> equal the size of the hole he should drill. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-54ad081a71da7a397507a00172f71b6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"81\" style=\"vertical-align: -7px;\" \/> to see what size the hole should be.<\/td>\n<td><strong data-effect=\"bold\">Baking<\/strong>\u00a0 62. Kelsey needs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e89c4f69688b0dd6ab75a55841059de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> cup of sugar for the cookie recipe she wants to make. She only has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83dc4a903812856a369855508d0b2637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> cup of sugar and will borrow the rest from her neighbour. Let <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;\" \/> equal the amount of sugar she will borrow. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fda8d10ac724f2aaf3f9546c11fc82e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#115;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"71\" style=\"vertical-align: -6px;\" \/> to find the amount of sugar she should ask to borrow.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166494586239\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table>\n<tbody>\n<tr>\n<td>63. Write a word sentence that translates the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9de5f2ba489996a1bd6fe595155ff8ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#49;&#56;&#61;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" style=\"vertical-align: -4px;\" \/> and then make up an application that uses this equation in its solution.<\/td>\n<td>64. Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> a solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6b8240becd6d42ce7a01d7802e48f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#61;&#49;&#54;&#45;&#53;&#120;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" style=\"vertical-align: -1px;\" \/> How do you know?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h1>Answers<\/h1>\n<table>\n<tbody>\n<tr>\n<td>1. yes<\/td>\n<td>3. no<\/td>\n<td>5.<em data-effect=\"italics\"> x<\/em> = 5<\/td>\n<\/tr>\n<tr>\n<td>7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f88d651249a9805b0f6a04a399c09647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>9.<em data-effect=\"italics\"> p<\/em> = \u221211.7<\/td>\n<td>11.<em data-effect=\"italics\"> a<\/em> = 10<\/td>\n<\/tr>\n<tr>\n<td>13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee996768bbd76229f36be47e646367ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>15.<em data-effect=\"italics\"> y<\/em> = 13.8<\/td>\n<td>17.<em data-effect=\"italics\"> x<\/em> = \u221227<\/td>\n<\/tr>\n<tr>\n<td>19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-650d54138713966d85dd0c844fbe0503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>21. 17<\/td>\n<td>23. 8<\/td>\n<\/tr>\n<tr>\n<td>25. \u221220<\/td>\n<td>27. 2<\/td>\n<td>29. \u22121.7<\/td>\n<\/tr>\n<tr>\n<td>31. \u22122<\/td>\n<td>33. \u22124<\/td>\n<td>35. 6<\/td>\n<\/tr>\n<tr>\n<td>37. \u221241<\/td>\n<td>39.<em data-effect=\"italics\"> x<\/em> + (\u22125) = 33; <em data-effect=\"italics\">x<\/em> = 38<\/td>\n<td>41.y \u2212 3 = \u221219; <em data-effect=\"italics\">y<\/em> = \u221216<\/td>\n<\/tr>\n<tr>\n<td>43.<em data-effect=\"italics\"> p<\/em> + 8 = 52; <em data-effect=\"italics\">p<\/em> = 44<\/td>\n<td>45. 5<em data-effect=\"italics\">c<\/em> \u2212 4<em data-effect=\"italics\">c<\/em> = 60; 60<\/td>\n<td>47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75f0a413d86e999902c4cca90b3558b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"112\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>49. \u22129<em data-effect=\"italics\">m<\/em> + 10<em data-effect=\"italics\">m<\/em> = \u221225; <em data-effect=\"italics\">m<\/em> = \u221225<\/td>\n<td>51. Let <em data-effect=\"italics\">p<\/em> equal the number of pages read in the Psychology book 41 + <em data-effect=\"italics\">p<\/em> = 54. Jeff read pages in his Psychology book.<\/td>\n<td>53. Let <em data-effect=\"italics\">d<\/em> equal the daughter\u2019s age. d = 12 \u2212 5. Eva\u2019s daughter\u2019s age is 7 years old.<\/td>\n<\/tr>\n<tr>\n<td>55. 21 pounds<\/td>\n<td>57. 100.5 degrees<\/td>\n<td>59. &#36;121.19<\/td>\n<\/tr>\n<tr>\n<td>61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-615ab5d181f493c4b65d30a04e638817_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>63. 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 Using the Subtraction and Addition Properties of Equality\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","protected":false},"author":90,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-842","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/842","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\/842\/revisions"}],"predecessor-version":[{"id":843,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/842\/revisions\/843"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/842\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=842"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=842"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=842"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}