{"id":1126,"date":"2020-08-12T14:18:34","date_gmt":"2020-08-12T18:18:34","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-with-fraction-or-decimal-coefficients\/"},"modified":"2021-03-24T10:56:04","modified_gmt":"2021-03-24T14:56:04","slug":"solve-equations-with-fraction-or-decimal-coefficients","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-with-fraction-or-decimal-coefficients\/","title":{"raw":"5.4 Solve Equations with Fraction or Decimal Coefficients","rendered":"5.4 Solve Equations with Fraction or Decimal Coefficients"},"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 with fraction coefficients<\/li>\n \t<li>Solve equations with decimal coefficients<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 id=\"fs-id1166491051944\" data-type=\"note\">Solve Equations with Fraction Coefficients<\/h1>\n<div id=\"fs-id1166490779333\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1572424\">Let\u2019s use the General Strategy for Solving Linear Equations introduced earlier to solve the equation \\(\\frac{1}{8}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{1}{2}=\\frac{1}{4}\\).<\/p>\n\n<table id=\"eip-id1168468637854\" style=\"width: 100%;\" summary=\"The top line says one-eighth x plus one-half equals one-fourth. The next line says, \u201cTo isolate the x term, subtract one-half from both sides,\u201d and shows one-eighth x plus one-half minus a red one-half equals one-fourth minus a red one-half. The next line says, \u201cSimplify the left side,\u201d and shows one-eighth x equals one-fourth minus one-half. The next line says, \u201cChange the constants to equivalent fractions with the LCD,\u201d and shows one-eighth x equals one-fourth minus two-fourths. The next line says, \u201cSubtract,\u201d and shows one-eighth x equals negative one-fourth. The next line says, \u201cMultiply both sides by the reciprocal of one-eighth,\u201d and shows a red 8 over 1 times one-eighth x equals a red 8 over 1 times negative one-fourth. The next line says, \u201cDivide,\u201d and shows 12x over a red 12 equals 4.8 over a red 12. The last line says, \u201cSimplify,\u201d and shows x equals negative 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468303232\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_04_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>To isolate the \\(x\\) term, subtract \\(\\frac{1}{2}\\) from both sides.<\/td>\n<td><span id=\"eip-id1168468687553\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify the left side.<\/td>\n<td><span id=\"eip-id1168468503142\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Change the constants to equivalent fractions with the LCD.<\/td>\n<td><span id=\"eip-id1168468299044\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168468241289\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the reciprocal of \\(\\frac{1}{8}\\).<\/td>\n<td><span id=\"eip-id1168468223424\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468762413\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166498435623\">This method worked fine, but many students don\u2019t feel very confident when they see all those fractions. So we are going to show an alternate method to solve equations with fractions. This alternate method eliminates the fractions.<\/p>\n<p id=\"fs-id1807706\">We will apply the <span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span> and multiply both sides of an equation by the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. This process is called <em data-effect=\"italics\">clearing the equation of fractions<\/em>. Let\u2019s solve the same equation again, but this time use the method that clears the fractions.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491427594\" data-type=\"problem\">\n<p id=\"fs-id1166484085715\">Solve: \\(\\frac{1}{8}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{1}{2}=\\frac{1}{4}\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166498114957\" data-type=\"solution\">\n<table id=\"eip-id1168467351085\" style=\"width: 100%;\" summary=\"The top line says, \u201cFind the least common denominator of all the fractions in the equation,\u201d and shows one-eighth x plus one-half equals one-fourth and LCD equals 8. The next line says, \u201cMultiply both sides of the equation by that LCD, 8. This clears the fractions,\u201d and shows a red 8 times each side of the original equation. The next line says, \u201cUse the Distributive Property. Simplify - and notice, no more fractions!\u201d Beside that is 8 times one-eighth x plus 8 times one-half equals 8 and one-fourth, then x plus 4 equals 2. The next line says, \u201cSolve using the General Strategy for Solving Linear Equations,\u201d and shows x plus 4 minus a red 4 equals 2 minus a red 4. The last step says, \u201cCheck. Let x equal negative 2.\u201d Beside that is the original equation followed by one-eighth times a red negative 2 plus one-half, equal sign with a question mark, one-fourth. Below that is negative 2 over 8 plus one-half, equal sign with a question mark, one-fourth. Below that is negative 2 over 8 plus 4 over 8, equal sign with a question mark, one-fourth. Below that is 2 over 8, equal sign with a question mark, one-fourth. The last line says one-fourth equals one-fourth.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468607429\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by that LCD, 8. This clears the fractions.<\/td>\n<td><span id=\"eip-id1168468515555\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468556552\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 and notice, no more fractions!<\/td>\n<td><span id=\"eip-id1168468649581\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve using the General Strategy for Solving Linear Equations.<\/td>\n<td><span id=\"eip-id1168468283150\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_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-id1168468444919\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\">Check: Let \\(x=-2\\)<\/td>\n<td><span id=\"eip-id1168468473387\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490916994\" data-type=\"problem\">\n<p id=\"fs-id1166484082904\">Solve: \\(\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{1}{2}=\\frac{5}{8}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1218908\">\\(x=\\frac{1}{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490820951\" data-type=\"problem\">\n<p id=\"fs-id1492200\">Solve: \\(\\frac{1}{6}\\phantom{\\rule{0.1em}{0ex}}y-\\frac{1}{3}=\\frac{1}{6}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166492788421\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490904286\"><em data-effect=\"italics\">y<\/em> = 3<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166491051648\">Notice in <a class=\"autogenerated-content\" href=\"#fs-id1360468\">(Figure)<\/a> that once we cleared the equation of fractions, the equation was like those we solved earlier in this chapter. We changed the problem to one we already knew how to solve! We then used the General Strategy for Solving Linear Equations.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Solve Equations with Fraction Coefficients by Clearing the Fractions<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168466140919\" class=\"stepwise\" type=\"1\">\n \t<li>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/li>\n \t<li>Multiply both sides of the equation by that LCD. This clears the fractions.<\/li>\n \t<li>Solve using the General Strategy for Solving Linear Equations.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1736703\" 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 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492527250\" data-type=\"problem\">\n<p id=\"fs-id1480388\">Solve: \\(7=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}x\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166479044172\" data-type=\"solution\">\n<p id=\"fs-id1166491296765\">We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.<\/p>\n\n<table id=\"eip-id1168468606496\" style=\"width: 100%;\" summary=\"The top line says \u201cThe LCD is 12\u201d and shows the equation 7 equals one-half x plus three-fourths x minus two-thirds x. The next line says, \u201cMultiply both sides of the equation by 12,\u201d and shows a red 12 times each side of the original equation. The next line says, \u201cDistribute,\u201d and shows 12 times 7 equals 12 times one-half x plus 12 times three-fourths x minus 12 times two-thirds x. The next line says, \u201cSimplify - and notice, no more fractions!\u201d Beside that is 84 equals 6x plus 9x minus 8x. The next line says, \u201cCombine like terms,\u201d and shows 84 equals 7x. The next line says, \u201cDivide by 7,\u201d and shows 84 over a red 7 equals 7x over a red 7. The next line says, \u201cSimplify,\u201d and shows 12 equals x. The last step says, \u201cCheck: Let x equal 12.\u201d Beside that is the original equation. Below that is 7 followed by an equal sign with a question mark, then one-half times a red 12 plus three-fourths times a red 12 minus two-thirds times a red 12. Bellow that is 7 followed by an equal sign with a question mark, then 6 plus 9 minus 8. The last line says 7 equals 7, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468769008\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by 12.<\/td>\n<td><span id=\"eip-id1168468769024\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468242412\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 and notice, no more fractions!<\/td>\n<td><span id=\"eip-id1168468715783\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168467289944\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 7.<\/td>\n<td><span id=\"eip-id1168467289961\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467374437\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=12\\).<\/td>\n<td><span id=\"eip-id1168467372853\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491403168\" data-type=\"problem\">\n<p id=\"fs-id1477105\">Solve: \\(6=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}v+\\frac{2}{5}\\phantom{\\rule{0.1em}{0ex}}v-\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}v\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1395277\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166497180077\"><em data-effect=\"italics\">v<\/em> = 40<\/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-id1166484085342\" data-type=\"problem\">\n<p id=\"fs-id1951658\">Solve: \\(-1=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}u+\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}u-\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}u\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1286862\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166492788296\"><em data-effect=\"italics\">u<\/em> = \u221212<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nIn the next example, we\u2019ll have variables and fractions on both sides of the equation.\n\n<\/div>\n<\/div>\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-id1166482442812\" data-type=\"problem\">\n<p id=\"fs-id1166490904704\">Solve: \\(x+\\frac{1}{3}=\\frac{1}{6}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{2}\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id2047530\" data-type=\"solution\">\n<table id=\"eip-id1168468770578\" style=\"width: 100%;\" summary=\"The top line says, \u201cFind the LCD of all fractions in the equation,\u201d and shows x plus one-third equals one-sixth x minus one-half. The next line says, \u201cThe LCD is 6. Multiply both sides by the LCD,\u201d and shows a red 6 times each side of the original equation. The next step says, \u201cDistribute,\u201d and shows 6x plus 6 times one-third equals 6 times one-sixth x minus 6 times one-half. The next step says, \u201cSimplify - no more fractions!\u201d and shows 6x plus 2 equals x minus 3. The next line says, \u201cSubtract x from both sides,\u201d and shows 6x minus a red x plus 2 equals x minus a red x minus 3. The next line says, \u201cSimplify,\u201d and shows 5x plus 2 equals negative 3. The next line says, \u201cSubtract 2 from both sides,\u201d and shows 5x plus 2 minus a red 2 equals negative 3 minus a red 2. The next line says, \u201cSimplify,\u201d and shows 5x equals negative 5. The next line says, \u201cDivide by 5,\u201d and shows 5x over a red 5 equals negative 5 over a red 5. The next line says, \u201cSimplify,\u201d and shows x equals negative 1. The next line says, \u201cCheck,\u201d and shows the original equation. The following line says, \u201cSubstitute x equals negative 1.\u201d Beside that is a red negative 1 plus one-third followed by an equal sign with a question mark, then one-sixth times a red negative 1 minus one-half. Below that is negative 1 plus one-third followed by an equal sign with a question mark, then negative one-sixth minus one-half. Below that is negative 3 over 3 plus 1 over 3 followed by an equal sign with a question mark, then negative 1 over 6 minus 3 over 6. Below that is negative 2 over 3 followed by an equal sign with a question mark, then negative 4 over 6. The last line says negative 2 over 3 equals negative 2 over 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the LCD of all the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468529936\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD.<\/td>\n<td><span id=\"eip-id1168468282603\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468282620\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 no more fractions!<\/td>\n<td><span id=\"eip-id1168467223401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(x\\) from both sides.<\/td>\n<td><span id=\"eip-id1168467314426\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_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-id1168467263801\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 2 from both sides.<\/td>\n<td><span id=\"eip-id1168467263817\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468736475\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 5.<\/td>\n<td><span id=\"eip-id1168468368873\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466049401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute \\(x=-1\\).<\/td>\n<td><span id=\"eip-id1168467359042\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id833062\" data-type=\"problem\">\n<p id=\"fs-id1166498432755\">Solve: \\(a+\\frac{3}{4}=\\frac{3}{8}\\phantom{\\rule{0.1em}{0ex}}a-\\frac{1}{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166498435488\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166491265399\"><em data-effect=\"italics\">a<\/em> = \u22122<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1424798\" data-type=\"problem\">\n<p id=\"fs-id1556117\">Solve: \\(c+\\frac{3}{4}=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}c-\\frac{1}{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1497888\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166491053314\"><em data-effect=\"italics\">c<\/em> = \u22122<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nIn <a href=\"#fs-id1341867\">(Figure)<\/a>, we\u2019ll start by using the Distributive Property. This step will clear the fractions right away!\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1732124\" data-type=\"problem\">\n<p id=\"fs-id1166488300088\">Solve: \\(1=\\frac{1}{2}\\left(4x+2\\right)\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166492761836\" data-type=\"solution\">\n<table id=\"eip-id1168469839370\" style=\"width: 100%;\" summary=\"The top line says 1 equals one-half times parentheses 4x plus 2. The next line says, \u201cDistribute,\u201d and shows 1 equals one-half times 4x plus one-half times 2. The next line says, \u201cSimplify. Now there are no fractions to clear!\u201d Beside that is 1 equals 2x plus 1. The next line says, \u201cSubtract 1 from both sides,\u201d and shows 1 minus a red 1 equals 2x plus 1 minus a red 1. The next line says, \u201cSimplify,\u201d and shows 0 equals 2x. The next line says, \u201cDivide by 2,\u201d and shows 0 over a red 2 equals 2x over a red 2. The next line says, \u201cSimplify,\u201d and shows 0 equals x. The last step says, \u201cCheck: Let x equal 0,\u201d and shows the original equation. Below that is 1 followed by an equal sign with a question mark, then one-half times parentheses 4 times a red 0 plus 2. Below that is 1 followed by an equal sign with a question mark, then one-half times 2. Below that is a 1 followed by an equal sign with a question mark, then 2 over 2. The last line says 1 equals 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466318642\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168466318657\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify. Now there are no fractions to clear!<\/td>\n<td><span id=\"eip-id1168469660114\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 1 from both sides.<\/td>\n<td><span id=\"eip-id1168469630509\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466333364\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 2.<\/td>\n<td><span id=\"eip-id1168466121763\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466690860\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=0\\).<\/td>\n<td><span id=\"eip-id1168466216328\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1332086\" data-type=\"problem\">\n\nSolve: \\(-11=\\frac{1}{2}\\left(6p+2\\right)\\).\n\n<\/div>\n<div id=\"fs-id1166491265601\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166497370295\"><em data-effect=\"italics\">p<\/em> = \u22124<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491298328\" data-type=\"problem\">\n<p id=\"fs-id1956784\">Solve: \\(8=\\frac{1}{3}\\left(9q+6\\right)\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490874403\"><em data-effect=\"italics\">q<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1512200\">Many times, there will still be fractions, even after distributing.<\/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-id1166494771210\" data-type=\"problem\">\n<p id=\"fs-id1166498435655\">Solve: \\(\\frac{1}{2}\\left(y-5\\right)=\\frac{1}{4}\\left(y-1\\right)\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1425420\" data-type=\"solution\">\n<table id=\"eip-id1168468274761\" style=\"width: 100%;\" summary=\"The top line says one-half times parentheses y minus 5 equals one-fourth times parentheses y minus 1. The next line says, \u201cDistribute,\u201d and shows one-half times y minus one-half times 5 equals one-fourth times y minus one-fourth times 1. The next line says, \u201cSimplify,\u201d and shows one-half y minus 5 over 2 equals one-fourth y minus one-fourth. The next step says, \u201cMultiply by the LCD, 4,\u201d and shows a red 4 times each side. The next step says, \u201cDistribute,\u201d and shows 4 times one-half y minus 4 times 5 over 2 equals 4 times one-fourth y minus 4 times one-fourth. The next line says, \u201cSimplify,\u201d and shows 2y minus 10 equals y minus 1. The next line says, \u201cCollect the y terms to the left,\u201d and shows 2y minus 10 minus a red y equals y minus 1 minus a red y. The next line says, \u201cSimplify,\u201d and shows y minus 10 equals negative 1. The next line says, \u201cCollect the constants to the right,\u201d and shows y minus 10 plus a red 10 equals negative 1 plus a red 10. The next line says, \u201cSimplify,\u201d and shows y equals 9. The last step says, \u201cCheck. Substitute: 9 for y,\u201d and shows the original equation. Below that is one-half times parentheses red 9 minus 5, equal sign with a question mark, one-fourth times parentheses red 9 minus 1. Below that is one-half times 4, equal sign with a question mark, one-fourth times 8, then 2 equals 2 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467438640\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468710108\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_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-id1168468710125\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply by the LCD, 4.<\/td>\n<td><span id=\"eip-id1168468710142\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168467196225\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_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-id1168467196242\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the \\(y\\) terms to the left.<\/td>\n<td><span id=\"eip-id1168467268019\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467268036\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the constants to the right.<\/td>\n<td><span id=\"eip-id1168468535485\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468535502\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute \\(9\\) for \\(y\\).<\/td>\n<td><span id=\"eip-id1168467129797\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166497362535\">Solve: \\(\\frac{1}{5}\\left(n+3\\right)=\\frac{1}{4}\\left(n+2\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1249251\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490863410\"><em data-effect=\"italics\">n<\/em> = 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1515018\" data-type=\"problem\">\n<p id=\"fs-id1527526\">Solve: \\(\\frac{1}{2}\\left(m-3\\right)=\\frac{1}{4}\\left(m-7\\right)\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1111963\"><em data-effect=\"italics\">m<\/em> = \u22121<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations with Decimal Coefficients<\/h1>\n<\/div>\n<div id=\"fs-id1166489101367\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166497416928\">Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But decimals are really another way to represent fractions. For example, \\(0.3=\\frac{3}{10}\\) and \\(0.17=\\frac{17}{100}\\). So, when we have an equation with decimals, we can use the same process we used to clear fractions\u2014multiply both sides of the equation by the <span class=\"no-emphasis\" data-type=\"term\">least common denominator<\/span>.<\/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-id757964\" data-type=\"problem\">\n<p id=\"fs-id1166484059532\">Solve: \\(0.8x-5=7\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166483694392\" data-type=\"solution\">\n\nThe only decimal in the equation is \\(0.8\\). Since \\(0.8=\\frac{8}{10}\\), the LCD is \\(10\\). We can multiply both sides by \\(10\\) to clear the decimal.\n<table id=\"eip-id1168467123212\" style=\"width: 100%;\" summary=\"The first line says 0.8x minus 5 equals 7. The next line says, \u201cMultiply both sides by the LCD,\u201d and shows both sides being multiplied by a red 10. The next line says, \u201cDistribute,\u201d and shows 10 times 0.8x minus 10 times 5 equals 10 times 7. The next line say, \u201cMultiply, and notice, no more decimals!\u201d Beside that is 8x minus 50 equals 70. The next line says, \u201cAdd 50 to get all constants to the right,\u201d and shows 8x minus 50 plus a red 50 equals 70 plus a red 50. The next line says, \u201cSimplify,\u201d and shows 8x equals 120. The next line says, \u201cDivide both sides by 8,\u201d and shows 8x over a red 8 equals 120 over a red 8. The next line says, \u201cSimplify,\u201d and shows x equals 15. The last step says, \u201cCheck. Let x equal 15.\u201d Beside that is 0.8 times a red 15 minus 5 equals 7, then 12 minus 5 equals 7, then 7 equals 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469717019\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466176164\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td data-align=\"right\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply, and notice, no more decimals!<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469856396\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 50 to get all constants to the right.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466113856\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469866706\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 8.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466076010\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469479703\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=15\\).<\/td>\n<td><span id=\"eip-id1168469484813\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nSolve: \\(0.6x-1=11\\).\n\n<\/div>\n<div id=\"fs-id1166497457871\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166497417096\"><em data-effect=\"italics\">x<\/em> = 20<\/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-id1166482427198\" data-type=\"problem\">\n<p id=\"fs-id1561222\">Solve: \\(1.2x-3=9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166497145924\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1416813\"><em data-effect=\"italics\">x<\/em> = 10<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1430641\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166497293847\" data-type=\"exercise\">\n<div data-type=\"problem\">\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-id1455775\" data-type=\"problem\">\n<p id=\"fs-id1547593\">Solve: \\(0.06x+0.02=0.25x-1.5\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166493762755\" data-type=\"solution\">\n<p id=\"fs-id1451821\">Look at the decimals and think of the equivalent fractions.<\/p>\n<p id=\"fs-id1734698\">\\(0.06=\\frac{6}{100},\\phantom{\\rule{1em}{0ex}}0.02=\\frac{2}{100},\\phantom{\\rule{1em}{0ex}}0.25=\\frac{25}{100},\\phantom{\\rule{1em}{0ex}}1.5=1\\frac{5}{10}\\)<\/p>\n<p id=\"fs-id1166497193424\">Notice, the LCD is \\(100\\).<\/p>\n<p id=\"fs-id1166492788308\">By multiplying by the LCD we will clear the decimals.<\/p>\n\n<table id=\"eip-id1168466076129\" style=\"width: 100%;\" summary=\"The top line says 0.06x plus 0.02 equals 0.25x minus 1.5. The next step says, \u201cMultiply both sides by 100,\u201d and shows a red 100 times both sides. The next step says, \u201cDistribute,\u201d and shows 100 times 0.06x plus 100 times 0.02 equals 100 times 0.25x minus 100 times 1.5. The next line says, \u201cMultiply, and now we have no more decimals,\u201d and shows 6x plus 2 equals 25x minus 150. The next line says, \u201cCollect the variables to the right,\u201d and shows 6x minus a red 6x plus 2 equals 25x minus a red 6x minus 150. The next line says, \u201cSimplify,\u201d and shows 2 equals 19x minus 150. The next line says, \u201cCollect the constants to the left,\u201d and shows 2 plus a red 150 equals 19x minus 150 plus a red 150. The next line says, \u201cSimplify,\u201d and shows 152 equals 19x. The next line says, \u201cDivide by 19,\u201d and shows 152 over a red 19 equals 19x over a red 19. The next line says, \u201cSimplify,\u201d and shows 8 equals x. The last line says, \u201cCheck: Let x equal 8,\u201d and shows 0.06 times a red 8 plus 0.02 equals 0.25 times a red 8 minus 1.5. Below that is 0.48 plus 0.02 equals 2.00 minus 1.5. The last line says 0.50 equals 0.50.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468585245\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 100.<\/td>\n<td><span id=\"eip-id1168467318224\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168467318241\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply, and now no more decimals.<\/td>\n<td><span id=\"eip-id1168467117747\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the variables to the right.<\/td>\n<td><span id=\"eip-id1168467117764\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_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-id1168467164551\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the constants to the left.<\/td>\n<td><span id=\"eip-id1168467164568\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467164584\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 19.<\/td>\n<td><span id=\"eip-id1168468585228\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467662562\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=8\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168467298894\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166497443816\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1444543\" data-type=\"exercise\">\n<div id=\"fs-id1166482427198\" data-type=\"problem\">\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-id1480177\" data-type=\"problem\">\n<p id=\"fs-id1166491410540\">Solve: \\(0.14h+0.12=0.35h-2.4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491055867\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166488294365\"><em data-effect=\"italics\">h<\/em> = 12<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1208806\" data-type=\"problem\">\n<p id=\"fs-id1627355\">Solve: \\(0.65k-0.1=0.4k-0.35\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1953706\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1524254\"><em data-effect=\"italics\">k<\/em> = \u22121<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nThe next example uses an equation that is typical of the ones we will see in the money applications in the next chapter. Notice that we will distribute the decimal first before we clear all decimals in the equation.\n\n<\/div>\n<\/div>\n<\/div>\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-id1377535\" data-type=\"problem\">\n<p id=\"fs-id1242257\">Solve: \\(0.25x+0.05\\left(x+3\\right)=2.85\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1435379\" data-type=\"solution\">\n<table id=\"eip-id1168466031358\" style=\"width: 100%;\" summary=\"The top line says 0.25x plus 0.05 times parentheses x plus 3 equals 2.85. The next line says, \u201cDistribute first,\u201d and shows 0.25x plus 0.05x plus 0.15 equals 2.85. The next line says, \u201cCombine like terms,\u201d and shows 0.30x plus 0.15 equals 2.85. The next line says, \u201cTo clear decimals, multiply by 100,\u201d and shows a red 100 times parentheses 0.30x plus 0.15 equals a red 100 times 2.85. The next line says, \u201cDistribute,\u201d and shows 30x plus 15 equals 285. The next line says, \u201cSubtract 15 from both sides,\u201d and shows 30x plus 15 minus a red 15 equals 285 minus a red 15. The next line says, \u201cSimplify,\u201d and shows 30x equals 270. The next line says, \u201cDivide by 30,\u201d and shows 30x over a red 30 equals 270 over a red 30. The next line says \u201cSimplify\u201d and shows x equals 9. The next line says, \u201cCheck,\u201d and shows the original equation. Below that is \u201cLet x equal 9\u201d and 0.25 times a red 9 plus 0.05 times parentheses red 9 plus 3, equal sign with a question mark, 2.85. Below that is 2.25 plus 0.05 times 12, equal sign with a question mark, 2.85. Below that is 2.25 plus 0.60 followed by an equal sign with a question mark, then 2.85. The last line shows 2.85 equals 2.85.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469693745\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute first.<\/td>\n<td><span id=\"eip-id1168469693762\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469744084\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>To clear decimals, multiply by 100.<\/td>\n<td><span id=\"eip-id1168469744102\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469744119\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 15 from both sides.<\/td>\n<td><span id=\"eip-id1168466012769\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466012786\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 30.<\/td>\n<td><span id=\"eip-id1168466636977\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466636994\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let \\(x=9\\).<\/td>\n<td><span id=\"eip-id1168469803943\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1766432\" data-type=\"problem\">\n<p id=\"fs-id1166476800717\">Solve: \\(0.25n+0.05\\left(n+5\\right)=2.95\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1724368\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166491228674\"><em data-effect=\"italics\">n<\/em> = 9<\/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 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1085091\">Solve: \\(0.10d+0.05\\left(d-5\\right)=2.15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1807431\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1518056\"><em data-effect=\"italics\">d<\/em> = 16<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul>\n \t<li><strong>Solve equations with fraction coefficients by clearing the fractions.<\/strong>\n<ol id=\"eip-id1170323900082\" class=\"stepwise\" type=\"1\">\n \t<li>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/li>\n \t<li>Multiply both sides of the equation by that LCD. This clears the fractions.<\/li>\n \t<li>Solve using the General Strategy for Solving Linear Equations.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practices Makes Perfect<\/h1>\n<div id=\"fs-id1166497278022\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1957264\">Solve equations with fraction coefficients<\/h2>\n<p id=\"eip-388\">In the following exercises, solve the equation by clearing the fractions.<\/p>\n\n<table border=\"0\">\n<tbody>\n<tr>\n<td>1. \\(\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{2}=-\\frac{3}{4}\\)<\/td>\n<td>2. \\(\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{2}=\\frac{1}{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>3. \\(\\frac{5}{6}\\phantom{\\rule{0.1em}{0ex}}y-\\frac{2}{3}=-\\frac{3}{2}\\)<\/td>\n<td>4. \\(\\frac{5}{6}\\phantom{\\rule{0.1em}{0ex}}y-\\frac{1}{3}=-\\frac{7}{6}\\)<\/td>\n<\/tr>\n<tr>\n<td>5. \\(\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}a+\\frac{3}{8}=\\frac{3}{4}\\)<\/td>\n<td>6. \\(\\frac{5}{8}\\phantom{\\rule{0.1em}{0ex}}b+\\frac{1}{2}=-\\frac{3}{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>7. \\(2=\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}x\\)<\/td>\n<td>8. \\(2=\\frac{3}{5}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{2}{5}\\phantom{\\rule{0.1em}{0ex}}x\\)<\/td>\n<\/tr>\n<tr>\n<td>9. \\(\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}m-\\frac{4}{5}\\phantom{\\rule{0.1em}{0ex}}m+\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}m=-1\\)<\/td>\n<td>10. \\(\\frac{5}{6}\\phantom{\\rule{0.1em}{0ex}}n-\\frac{1}{4}\\phantom{\\rule{0.1em}{0ex}}n-\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}n=-2\\)<\/td>\n<\/tr>\n<tr>\n<td>11. \\(x+\\frac{1}{2}=\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{2}\\)<\/td>\n<td>12. \\(x+\\frac{3}{4}=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{5}{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>13. \\(\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}w+\\frac{5}{4}=w-\\frac{1}{4}\\)<\/td>\n<td>14. \\(\\frac{3}{2}\\phantom{\\rule{0.1em}{0ex}}z+\\frac{1}{3}=z-\\frac{2}{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>15. \\(\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{1}{4}=\\frac{1}{12}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{1}{6}\\)<\/td>\n<td>16. \\(\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}a-\\frac{1}{4}=\\frac{1}{6}\\phantom{\\rule{0.1em}{0ex}}a+\\frac{1}{12}\\)<\/td>\n<\/tr>\n<tr>\n<td>17. \\(\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}b+\\frac{1}{5}=\\frac{2}{5}\\phantom{\\rule{0.1em}{0ex}}b-\\frac{3}{5}\\)<\/td>\n<td>18. \\(\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}x+\\frac{2}{5}=\\frac{1}{5}\\phantom{\\rule{0.1em}{0ex}}x-\\frac{2}{5}\\)<\/td>\n<\/tr>\n<tr>\n<td>19. \\(1=\\frac{1}{6}\\left(12x-6\\right)\\)<\/td>\n<td>20. \\(1=\\frac{1}{5}\\left(15x-10\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>21. \\(\\frac{1}{4}\\left(p-7\\right)=\\frac{1}{3}\\left(p+5\\right)\\)<\/td>\n<td>22. \\(\\frac{1}{5}\\left(q+3\\right)=\\frac{1}{2}\\left(q-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>23. \\(\\frac{1}{2}\\left(x+4\\right)=\\frac{3}{4}\\)<\/td>\n<td>24. \\(\\frac{1}{3}\\left(x+5\\right)=\\frac{5}{6}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166497276654\">Solve Equations with Decimal Coefficients<\/h2>\n<p id=\"eip-497\">In the following exercises, solve the equation by clearing the decimals.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>25. \\(0.6y+3=9\\)<\/td>\n<td>26. \\(0.4y-4=2\\)<\/td>\n<\/tr>\n<tr>\n<td>27. \\(3.6j-2=5.2\\)<\/td>\n<td>28. \\(2.1k+3=7.2\\)<\/td>\n<\/tr>\n<tr>\n<td>29. \\(0.4x+0.6=0.5x-1.2\\)<\/td>\n<td>30. \\(0.7x+0.4=0.6x+2.4\\)<\/td>\n<\/tr>\n<tr>\n<td>31. \\(0.23x+1.47=0.37x-1.05\\)<\/td>\n<td>32. \\(0.48x+1.56=0.58x-0.64\\)<\/td>\n<\/tr>\n<tr>\n<td>33. \\(0.9x-1.25=0.75x+1.75\\)<\/td>\n<td>34. \\(1.2x-0.91=0.8x+2.29\\)<\/td>\n<\/tr>\n<tr>\n<td>35. \\(0.05n+0.10\\left(n+8\\right)=2.15\\)<\/td>\n<td>36. \\(0.05n+0.10\\left(n+7\\right)=3.55\\)<\/td>\n<\/tr>\n<tr>\n<td>37. \\(0.10d+0.25\\left(d+5\\right)=4.05\\)<\/td>\n<td>38. \\(0.10d+0.25\\left(d+7\\right)=5.25\\)<\/td>\n<\/tr>\n<tr>\n<td>39. \\(0.05\\left(q-5\\right)+0.25q=3.05\\)<\/td>\n<td>40. \\(0.05\\left(q-8\\right)+0.25q=4.10\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div 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\">Coins<\/strong>\u00a0 41. Taylor has \\(\\text{\\$2.00}\\) in dimes and pennies. The number of pennies is \\(2\\) more than the number of dimes. Solve the equation \\(0.10d+0.01\\left(d+2\\right)=2\\) for \\(d\\), the number of dimes.<\/td>\n<td><strong data-effect=\"bold\">Stamps 42.\u00a0<\/strong> Travis bought \\(\\text{\\$9.45}\\) worth of \\(\\text{49-cent}\\) stamps and \\(\\text{21-cent}\\) stamps. The number of \\(\\text{21-cent}\\) stamps was \\(5\\) less than the number of \\(\\text{49-cent}\\) stamps. Solve the equation \\(0.49s+0.21\\left(s-5\\right)=9.45\\) for \\(s\\), to find the number of \\(\\text{49-cent}\\) stamps Travis bought.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>43. Explain how to find the least common denominator of \\(\\frac{3}{8},\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6},\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\).<\/td>\n<td>44. If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?<\/td>\n<\/tr>\n<tr>\n<td>45. If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?<\/td>\n<td>46. In the equation \\(0.35x+2.1=3.85\\), what is the LCD? How do you know?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h1>Answers<\/h1>\n<\/div>\n<div data-depth=\"1\">\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. x = -1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. y = -1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. \\(a=\\frac{3}{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. x = 4<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. m = 20<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. x = -3<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. \\(w=\\frac{9}{4}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. x = 1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. b = 12<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. x = 1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. p = -41<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. \\(x=-\\frac{5}{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. y = 10<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. j = 2<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. x = 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. x = 18<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. x = 20<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. n = 9<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. d = 8<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. q = 11<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41 d = 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45.Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cSolve Equations with Fraction or Decimal Coefficients\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\n\n<\/div>","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 with fraction coefficients<\/li>\n<li>Solve equations with decimal coefficients<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 id=\"fs-id1166491051944\" data-type=\"note\">Solve Equations with Fraction Coefficients<\/h1>\n<div id=\"fs-id1166490779333\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1572424\">Let\u2019s use the General Strategy for Solving Linear Equations introduced earlier to solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23536bd7b70946f06b998bfbc0d4cdf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<table id=\"eip-id1168468637854\" style=\"width: 100%;\" summary=\"The top line says one-eighth x plus one-half equals one-fourth. The next line says, \u201cTo isolate the x term, subtract one-half from both sides,\u201d and shows one-eighth x plus one-half minus a red one-half equals one-fourth minus a red one-half. The next line says, \u201cSimplify the left side,\u201d and shows one-eighth x equals one-fourth minus one-half. The next line says, \u201cChange the constants to equivalent fractions with the LCD,\u201d and shows one-eighth x equals one-fourth minus two-fourths. The next line says, \u201cSubtract,\u201d and shows one-eighth x equals negative one-fourth. The next line says, \u201cMultiply both sides by the reciprocal of one-eighth,\u201d and shows a red 8 over 1 times one-eighth x equals a red 8 over 1 times negative one-fourth. The next line says, \u201cDivide,\u201d and shows 12x over a red 12 equals 4.8 over a red 12. The last line says, \u201cSimplify,\u201d and shows x equals negative 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468303232\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_08_04_024_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>To isolate 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;\" \/> term, subtract <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;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168468687553\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify the left side.<\/td>\n<td><span id=\"eip-id1168468503142\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Change the constants to equivalent fractions with the LCD.<\/td>\n<td><span id=\"eip-id1168468299044\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168468241289\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9de931d332a83dd3da0c1ba21347996c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468223424\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468762413\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_024_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166498435623\">This method worked fine, but many students don\u2019t feel very confident when they see all those fractions. So we are going to show an alternate method to solve equations with fractions. This alternate method eliminates the fractions.<\/p>\n<p id=\"fs-id1807706\">We will apply the <span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span> and multiply both sides of an equation by the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. This process is called <em data-effect=\"italics\">clearing the equation of fractions<\/em>. Let\u2019s solve the same equation again, but this time use the method that clears the fractions.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491427594\" data-type=\"problem\">\n<p id=\"fs-id1166484085715\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23536bd7b70946f06b998bfbc0d4cdf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166498114957\" data-type=\"solution\">\n<table id=\"eip-id1168467351085\" style=\"width: 100%;\" summary=\"The top line says, \u201cFind the least common denominator of all the fractions in the equation,\u201d and shows one-eighth x plus one-half equals one-fourth and LCD equals 8. The next line says, \u201cMultiply both sides of the equation by that LCD, 8. This clears the fractions,\u201d and shows a red 8 times each side of the original equation. The next line says, \u201cUse the Distributive Property. Simplify - and notice, no more fractions!\u201d Beside that is 8 times one-eighth x plus 8 times one-half equals 8 and one-fourth, then x plus 4 equals 2. The next line says, \u201cSolve using the General Strategy for Solving Linear Equations,\u201d and shows x plus 4 minus a red 4 equals 2 minus a red 4. The last step says, \u201cCheck. Let x equal negative 2.\u201d Beside that is the original equation followed by one-eighth times a red negative 2 plus one-half, equal sign with a question mark, one-fourth. Below that is negative 2 over 8 plus one-half, equal sign with a question mark, one-fourth. Below that is negative 2 over 8 plus 4 over 8, equal sign with a question mark, one-fourth. Below that is 2 over 8, equal sign with a question mark, one-fourth. The last line says one-fourth equals one-fourth.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468607429\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by that LCD, 8. This clears the fractions.<\/td>\n<td><span id=\"eip-id1168468515555\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Distributive Property.<\/td>\n<td><span id=\"eip-id1168468556552\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 and notice, no more fractions!<\/td>\n<td><span id=\"eip-id1168468649581\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve using the General Strategy for Solving Linear Equations.<\/td>\n<td><span id=\"eip-id1168468283150\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_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-id1168468444919\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-align=\"left\">Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><span id=\"eip-id1168468473387\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_025_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490916994\" data-type=\"problem\">\n<p id=\"fs-id1166484082904\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3db1dfca171d9d59574ab9daa5569c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1218908\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46a3660db7e8d7648aa7837763fdd17d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" 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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166490820951\" data-type=\"problem\">\n<p id=\"fs-id1492200\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3097fdc818c5539c4263bfe34f77d072_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166492788421\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490904286\"><em data-effect=\"italics\">y<\/em> = 3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166491051648\">Notice in <a class=\"autogenerated-content\" href=\"#fs-id1360468\">(Figure)<\/a> that once we cleared the equation of fractions, the equation was like those we solved earlier in this chapter. We changed the problem to one we already knew how to solve! We then used the General Strategy for Solving Linear Equations.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Solve Equations with Fraction Coefficients by Clearing the Fractions<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168466140919\" class=\"stepwise\" type=\"1\">\n<li>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/li>\n<li>Multiply both sides of the equation by that LCD. This clears the fractions.<\/li>\n<li>Solve using the General Strategy for Solving Linear Equations.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1736703\" 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 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166492527250\" data-type=\"problem\">\n<p id=\"fs-id1480388\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb95295e9bb76470fd84b6e4b3f6a9c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166479044172\" data-type=\"solution\">\n<p id=\"fs-id1166491296765\">We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.<\/p>\n<table id=\"eip-id1168468606496\" style=\"width: 100%;\" summary=\"The top line says \u201cThe LCD is 12\u201d and shows the equation 7 equals one-half x plus three-fourths x minus two-thirds x. The next line says, \u201cMultiply both sides of the equation by 12,\u201d and shows a red 12 times each side of the original equation. The next line says, \u201cDistribute,\u201d and shows 12 times 7 equals 12 times one-half x plus 12 times three-fourths x minus 12 times two-thirds x. The next line says, \u201cSimplify - and notice, no more fractions!\u201d Beside that is 84 equals 6x plus 9x minus 8x. The next line says, \u201cCombine like terms,\u201d and shows 84 equals 7x. The next line says, \u201cDivide by 7,\u201d and shows 84 over a red 7 equals 7x over a red 7. The next line says, \u201cSimplify,\u201d and shows 12 equals x. The last step says, \u201cCheck: Let x equal 12.\u201d Beside that is the original equation. Below that is 7 followed by an equal sign with a question mark, then one-half times a red 12 plus three-fourths times a red 12 minus two-thirds times a red 12. Bellow that is 7 followed by an equal sign with a question mark, then 6 plus 9 minus 8. The last line says 7 equals 7, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468769008\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides of the equation by 12.<\/td>\n<td><span id=\"eip-id1168468769024\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468242412\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 and notice, no more fractions!<\/td>\n<td><span id=\"eip-id1168468715783\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168467289944\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 7.<\/td>\n<td><span id=\"eip-id1168467289961\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467374437\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-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;\" \/>.<\/td>\n<td><span id=\"eip-id1168467372853\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_026_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491403168\" data-type=\"problem\">\n<p id=\"fs-id1477105\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91e5e23c1b25d50af9c74324a92fd4f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#118;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#118;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"141\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1395277\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497180077\"><em data-effect=\"italics\">v<\/em> = 40<\/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-id1166484085342\" data-type=\"problem\">\n<p id=\"fs-id1951658\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f59bdfeb9459e960c9ca89f45a8afbf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#117;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#117;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1286862\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166492788296\"><em data-effect=\"italics\">u<\/em> = \u221212<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>In the next example, we\u2019ll have variables and fractions on both sides of the equation.<\/p>\n<\/div>\n<\/div>\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-id1166482442812\" data-type=\"problem\">\n<p id=\"fs-id1166490904704\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e3c519b8ca886b3fa97464b108626f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id2047530\" data-type=\"solution\">\n<table id=\"eip-id1168468770578\" style=\"width: 100%;\" summary=\"The top line says, \u201cFind the LCD of all fractions in the equation,\u201d and shows x plus one-third equals one-sixth x minus one-half. The next line says, \u201cThe LCD is 6. Multiply both sides by the LCD,\u201d and shows a red 6 times each side of the original equation. The next step says, \u201cDistribute,\u201d and shows 6x plus 6 times one-third equals 6 times one-sixth x minus 6 times one-half. The next step says, \u201cSimplify - no more fractions!\u201d and shows 6x plus 2 equals x minus 3. The next line says, \u201cSubtract x from both sides,\u201d and shows 6x minus a red x plus 2 equals x minus a red x minus 3. The next line says, \u201cSimplify,\u201d and shows 5x plus 2 equals negative 3. The next line says, \u201cSubtract 2 from both sides,\u201d and shows 5x plus 2 minus a red 2 equals negative 3 minus a red 2. The next line says, \u201cSimplify,\u201d and shows 5x equals negative 5. The next line says, \u201cDivide by 5,\u201d and shows 5x over a red 5 equals negative 5 over a red 5. The next line says, \u201cSimplify,\u201d and shows x equals negative 1. The next line says, \u201cCheck,\u201d and shows the original equation. The following line says, \u201cSubstitute x equals negative 1.\u201d Beside that is a red negative 1 plus one-third followed by an equal sign with a question mark, then one-sixth times a red negative 1 minus one-half. Below that is negative 1 plus one-third followed by an equal sign with a question mark, then negative one-sixth minus one-half. Below that is negative 3 over 3 plus 1 over 3 followed by an equal sign with a question mark, then negative 1 over 6 minus 3 over 6. Below that is negative 2 over 3 followed by an equal sign with a question mark, then negative 4 over 6. The last line says negative 2 over 3 equals negative 2 over 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the LCD of all the fractions in the equation.<\/td>\n<td><span id=\"eip-id1168468529936\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD.<\/td>\n<td><span id=\"eip-id1168468282603\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468282620\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \u2014 no more fractions!<\/td>\n<td><span id=\"eip-id1168467223401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-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;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168467314426\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_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-id1168467263801\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 2 from both sides.<\/td>\n<td><span id=\"eip-id1168467263817\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468736475\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 5.<\/td>\n<td><span id=\"eip-id1168468368873\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466049401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168467359042\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_027_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id833062\" data-type=\"problem\">\n<p id=\"fs-id1166498432755\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05f1d3efc0369009c459e80e56212148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166498435488\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491265399\"><em data-effect=\"italics\">a<\/em> = \u22122<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1424798\" data-type=\"problem\">\n<p id=\"fs-id1556117\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-76916c1afdd749e09dc143d364775269_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1497888\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491053314\"><em data-effect=\"italics\">c<\/em> = \u22122<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>In <a href=\"#fs-id1341867\">(Figure)<\/a>, we\u2019ll start by using the Distributive Property. This step will clear the fractions right away!<\/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 id=\"fs-id1732124\" data-type=\"problem\">\n<p id=\"fs-id1166488300088\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-323d2545634ff56f90b068d3bc7ebf48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166492761836\" data-type=\"solution\">\n<table id=\"eip-id1168469839370\" style=\"width: 100%;\" summary=\"The top line says 1 equals one-half times parentheses 4x plus 2. The next line says, \u201cDistribute,\u201d and shows 1 equals one-half times 4x plus one-half times 2. The next line says, \u201cSimplify. Now there are no fractions to clear!\u201d Beside that is 1 equals 2x plus 1. The next line says, \u201cSubtract 1 from both sides,\u201d and shows 1 minus a red 1 equals 2x plus 1 minus a red 1. The next line says, \u201cSimplify,\u201d and shows 0 equals 2x. The next line says, \u201cDivide by 2,\u201d and shows 0 over a red 2 equals 2x over a red 2. The next line says, \u201cSimplify,\u201d and shows 0 equals x. The last step says, \u201cCheck: Let x equal 0,\u201d and shows the original equation. Below that is 1 followed by an equal sign with a question mark, then one-half times parentheses 4 times a red 0 plus 2. Below that is 1 followed by an equal sign with a question mark, then one-half times 2. Below that is a 1 followed by an equal sign with a question mark, then 2 over 2. The last line says 1 equals 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466318642\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168466318657\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify. Now there are no fractions to clear!<\/td>\n<td><span id=\"eip-id1168469660114\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 1 from both sides.<\/td>\n<td><span id=\"eip-id1168469630509\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466333364\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 2.<\/td>\n<td><span id=\"eip-id1168466121763\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466690860\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466216328\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_028_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1332086\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32e6d44b1fda239a51eba74716a4ab2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#112;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"129\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491265601\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497370295\"><em data-effect=\"italics\">p<\/em> = \u22124<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166491298328\" data-type=\"problem\">\n<p id=\"fs-id1956784\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebf6e2e4df6568166095c54c93302e43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490874403\"><em data-effect=\"italics\">q<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1512200\">Many times, there will still be fractions, even after distributing.<\/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-id1166494771210\" data-type=\"problem\">\n<p id=\"fs-id1166498435655\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f441eb3112286445e10355fdca4cd257_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"156\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1425420\" data-type=\"solution\">\n<table id=\"eip-id1168468274761\" style=\"width: 100%;\" summary=\"The top line says one-half times parentheses y minus 5 equals one-fourth times parentheses y minus 1. The next line says, \u201cDistribute,\u201d and shows one-half times y minus one-half times 5 equals one-fourth times y minus one-fourth times 1. The next line says, \u201cSimplify,\u201d and shows one-half y minus 5 over 2 equals one-fourth y minus one-fourth. The next step says, \u201cMultiply by the LCD, 4,\u201d and shows a red 4 times each side. The next step says, \u201cDistribute,\u201d and shows 4 times one-half y minus 4 times 5 over 2 equals 4 times one-fourth y minus 4 times one-fourth. The next line says, \u201cSimplify,\u201d and shows 2y minus 10 equals y minus 1. The next line says, \u201cCollect the y terms to the left,\u201d and shows 2y minus 10 minus a red y equals y minus 1 minus a red y. The next line says, \u201cSimplify,\u201d and shows y minus 10 equals negative 1. The next line says, \u201cCollect the constants to the right,\u201d and shows y minus 10 plus a red 10 equals negative 1 plus a red 10. The next line says, \u201cSimplify,\u201d and shows y equals 9. The last step says, \u201cCheck. Substitute: 9 for y,\u201d and shows the original equation. Below that is one-half times parentheses red 9 minus 5, equal sign with a question mark, one-fourth times parentheses red 9 minus 1. Below that is one-half times 4, equal sign with a question mark, one-fourth times 8, then 2 equals 2 followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467438640\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168468710108\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_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-id1168468710125\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply by the LCD, 4.<\/td>\n<td><span id=\"eip-id1168468710142\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168467196225\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_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-id1168467196242\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the <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;\" \/> terms to the left.<\/td>\n<td><span id=\"eip-id1168467268019\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467268036\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the constants to the right.<\/td>\n<td><span id=\"eip-id1168468535485\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468535502\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> for <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;\" \/>.<\/td>\n<td><span id=\"eip-id1168467129797\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_029_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166497362535\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e5ea49efc0a99ced67ed704e68ff33d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1249251\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490863410\"><em data-effect=\"italics\">n<\/em> = 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1515018\" data-type=\"problem\">\n<p id=\"fs-id1527526\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d8f7c25d01ab2c0f6b6b1d65d5e47b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"168\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1111963\"><em data-effect=\"italics\">m<\/em> = \u22121<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations with Decimal Coefficients<\/h1>\n<\/div>\n<div id=\"fs-id1166489101367\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166497416928\">Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But decimals are really another way to represent fractions. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b4acb81ec832fb17530f4fa9eadd3e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-014f53d05a793ee9b322789141281640_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#55;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"78\" style=\"vertical-align: -7px;\" \/>. So, when we have an equation with decimals, we can use the same process we used to clear fractions\u2014multiply both sides of the equation by the <span class=\"no-emphasis\" data-type=\"term\">least common denominator<\/span>.<\/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-id757964\" data-type=\"problem\">\n<p id=\"fs-id1166484059532\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27b53e3db3076a52df8bafc0ce530779_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#56;&#120;&#45;&#53;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"96\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166483694392\" data-type=\"solution\">\n<p>The only decimal in the equation is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e4419032e9b2a7c997243dc95aced4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/>. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63b1596b738efc3bd70750a36b5f2a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#56;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/>, the LCD is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>. We can multiply both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> to clear the decimal.<\/p>\n<table id=\"eip-id1168467123212\" style=\"width: 100%;\" summary=\"The first line says 0.8x minus 5 equals 7. The next line says, \u201cMultiply both sides by the LCD,\u201d and shows both sides being multiplied by a red 10. The next line says, \u201cDistribute,\u201d and shows 10 times 0.8x minus 10 times 5 equals 10 times 7. The next line say, \u201cMultiply, and notice, no more decimals!\u201d Beside that is 8x minus 50 equals 70. The next line says, \u201cAdd 50 to get all constants to the right,\u201d and shows 8x minus 50 plus a red 50 equals 70 plus a red 50. The next line says, \u201cSimplify,\u201d and shows 8x equals 120. The next line says, \u201cDivide both sides by 8,\u201d and shows 8x over a red 8 equals 120 over a red 8. The next line says, \u201cSimplify,\u201d and shows x equals 15. The last step says, \u201cCheck. Let x equal 15.\u201d Beside that is 0.8 times a red 15 minus 5 equals 7, then 12 minus 5 equals 7, then 7 equals 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469717019\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466176164\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td data-align=\"right\"><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_04_030_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply, and notice, no more decimals!<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469856396\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add 50 to get all constants to the right.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466113856\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469866706\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 8.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168466076010\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><span id=\"eip-id1168469479703\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-386f25850ce593fc3cd4d4564e3709e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469484813\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_030_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-180025e0e5ebf3ec10c3558e46cea16f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;&#120;&#45;&#49;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"104\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166497457871\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166497417096\"><em data-effect=\"italics\">x<\/em> = 20<\/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-id1166482427198\" data-type=\"problem\">\n<p id=\"fs-id1561222\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26770662f8ccf6e91345e0c05016f93a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#120;&#45;&#51;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"95\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166497145924\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1416813\"><em data-effect=\"italics\">x<\/em> = 10<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1430641\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166497293847\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1455775\" data-type=\"problem\">\n<p id=\"fs-id1547593\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-333e22bf9a4c66028fdd08b320d9ba3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#54;&#120;&#43;&#48;&#46;&#48;&#50;&#61;&#48;&#46;&#50;&#53;&#120;&#45;&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"204\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166493762755\" data-type=\"solution\">\n<p id=\"fs-id1451821\">Look at the decimals and think of the equivalent fractions.<\/p>\n<p id=\"fs-id1734698\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a85e35294411cead90e86a12c1f40dba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#54;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#48;&#48;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#48;&#50;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#49;&#48;&#48;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#46;&#50;&#53;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#48;&#48;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#46;&#53;&#61;&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"387\" style=\"vertical-align: -7px;\" \/><\/p>\n<p id=\"fs-id1166497193424\">Notice, the LCD is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1166492788308\">By multiplying by the LCD we will clear the decimals.<\/p>\n<table id=\"eip-id1168466076129\" style=\"width: 100%;\" summary=\"The top line says 0.06x plus 0.02 equals 0.25x minus 1.5. The next step says, \u201cMultiply both sides by 100,\u201d and shows a red 100 times both sides. The next step says, \u201cDistribute,\u201d and shows 100 times 0.06x plus 100 times 0.02 equals 100 times 0.25x minus 100 times 1.5. The next line says, \u201cMultiply, and now we have no more decimals,\u201d and shows 6x plus 2 equals 25x minus 150. The next line says, \u201cCollect the variables to the right,\u201d and shows 6x minus a red 6x plus 2 equals 25x minus a red 6x minus 150. The next line says, \u201cSimplify,\u201d and shows 2 equals 19x minus 150. The next line says, \u201cCollect the constants to the left,\u201d and shows 2 plus a red 150 equals 19x minus 150 plus a red 150. The next line says, \u201cSimplify,\u201d and shows 152 equals 19x. The next line says, \u201cDivide by 19,\u201d and shows 152 over a red 19 equals 19x over a red 19. The next line says, \u201cSimplify,\u201d and shows 8 equals x. The last line says, \u201cCheck: Let x equal 8,\u201d and shows 0.06 times a red 8 plus 0.02 equals 0.25 times a red 8 minus 1.5. Below that is 0.48 plus 0.02 equals 2.00 minus 1.5. The last line says 0.50 equals 0.50.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468585245\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 100.<\/td>\n<td><span id=\"eip-id1168467318224\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168467318241\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply, and now no more decimals.<\/td>\n<td><span id=\"eip-id1168467117747\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the variables to the right.<\/td>\n<td><span id=\"eip-id1168467117764\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_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-id1168467164551\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Collect the constants to the left.<\/td>\n<td><span id=\"eip-id1168467164568\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467164584\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 19.<\/td>\n<td><span id=\"eip-id1168468585228\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168467662562\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-10-1.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-1dc438da70f358c2eb1bf64a8b7ea4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168467298894\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_031_img-11-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166497443816\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1444543\" data-type=\"exercise\">\n<div id=\"fs-id1166482427198\" data-type=\"problem\">\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-id1480177\" data-type=\"problem\">\n<p id=\"fs-id1166491410540\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc0d35ada2eb5ced9ff1856618080081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#52;&#104;&#43;&#48;&#46;&#49;&#50;&#61;&#48;&#46;&#51;&#53;&#104;&#45;&#50;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"205\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491055867\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166488294365\"><em data-effect=\"italics\">h<\/em> = 12<\/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-id1208806\" data-type=\"problem\">\n<p id=\"fs-id1627355\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-171c4d5df1c8da36b78a11f513b326fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;&#53;&#107;&#45;&#48;&#46;&#49;&#61;&#48;&#46;&#52;&#107;&#45;&#48;&#46;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"194\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1953706\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1524254\"><em data-effect=\"italics\">k<\/em> = \u22121<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>The next example uses an equation that is typical of the ones we will see in the money applications in the next chapter. Notice that we will distribute the decimal first before we clear all decimals in the equation.<\/p>\n<\/div>\n<\/div>\n<\/div>\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-id1377535\" data-type=\"problem\">\n<p id=\"fs-id1242257\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-158873e9a49e1a13afc5bc363aabc476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#120;&#43;&#48;&#46;&#48;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#46;&#56;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"207\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1435379\" data-type=\"solution\">\n<table id=\"eip-id1168466031358\" style=\"width: 100%;\" summary=\"The top line says 0.25x plus 0.05 times parentheses x plus 3 equals 2.85. The next line says, \u201cDistribute first,\u201d and shows 0.25x plus 0.05x plus 0.15 equals 2.85. The next line says, \u201cCombine like terms,\u201d and shows 0.30x plus 0.15 equals 2.85. The next line says, \u201cTo clear decimals, multiply by 100,\u201d and shows a red 100 times parentheses 0.30x plus 0.15 equals a red 100 times 2.85. The next line says, \u201cDistribute,\u201d and shows 30x plus 15 equals 285. The next line says, \u201cSubtract 15 from both sides,\u201d and shows 30x plus 15 minus a red 15 equals 285 minus a red 15. The next line says, \u201cSimplify,\u201d and shows 30x equals 270. The next line says, \u201cDivide by 30,\u201d and shows 30x over a red 30 equals 270 over a red 30. The next line says \u201cSimplify\u201d and shows x equals 9. The next line says, \u201cCheck,\u201d and shows the original equation. Below that is \u201cLet x equal 9\u201d and 0.25 times a red 9 plus 0.05 times parentheses red 9 plus 3, equal sign with a question mark, 2.85. Below that is 2.25 plus 0.05 times 12, equal sign with a question mark, 2.85. Below that is 2.25 plus 0.60 followed by an equal sign with a question mark, then 2.85. The last line shows 2.85 equals 2.85.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469693745\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute first.<\/td>\n<td><span id=\"eip-id1168469693762\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168469744084\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>To clear decimals, multiply by 100.<\/td>\n<td><span id=\"eip-id1168469744102\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168469744119\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract 15 from both sides.<\/td>\n<td><span id=\"eip-id1168466012769\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466012786\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide by 30.<\/td>\n<td><span id=\"eip-id1168466636977\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466636994\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-09-1.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-300a345ef7b973d34879ac8e90555390_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168469803943\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_04_032_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1766432\" data-type=\"problem\">\n<p id=\"fs-id1166476800717\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc8fcd7bb2c93e0286322b7996b4b80e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#110;&#43;&#48;&#46;&#48;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#46;&#57;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"208\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1724368\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491228674\"><em data-effect=\"italics\">n<\/em> = 9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1085091\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfaa577065712300e7fa4026bfb5920d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#48;&#100;&#43;&#48;&#46;&#48;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#100;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#46;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"205\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1807431\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1518056\"><em data-effect=\"italics\">d<\/em> = 16<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul>\n<li><strong>Solve equations with fraction coefficients by clearing the fractions.<\/strong>\n<ol id=\"eip-id1170323900082\" class=\"stepwise\" type=\"1\">\n<li>Find the least common denominator of <em data-effect=\"italics\">all<\/em> the fractions in the equation.<\/li>\n<li>Multiply both sides of the equation by that LCD. This clears the fractions.<\/li>\n<li>Solve using the General Strategy for Solving Linear Equations.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practices Makes Perfect<\/h1>\n<div id=\"fs-id1166497278022\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1957264\">Solve equations with fraction coefficients<\/h2>\n<p id=\"eip-388\">In the following exercises, solve the equation by clearing the fractions.<\/p>\n<table>\n<tbody>\n<tr>\n<td>1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5d2aea2b0c419a86401518f96f55354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1946814b920796adb6e18b8127f7d268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-489036e0ac9943fabfa24dac6eb1a671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb40ef00c939712756c45d7e43f0c992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49c02e99d126107f82cb72c233e0579a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f62ad8d15f971a17c3d9188b21e72cff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15b11a145e50bf01c0a18207580d7ff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d7e96519d1b9238685cbee7e1694dc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" 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-60cfec35e725ad01434eb5e6a7cc2957_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"171\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f709a13bd27f175cf907848e393262_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83e98a2f8ba3c894717a1dcb89f43a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5e6bbbe8e80112ffbca6827c7b6eae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46565ce45f109287bfb725fd84043cf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#119;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#61;&#119;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"124\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a96cbb1c3988ba314ace9f794632e28b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#122;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#122;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" 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-0cf6685fb84ae019198e3631073673f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"137\" style=\"vertical-align: -7px;\" \/><\/td>\n<td>16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-072f1865575b27ea77a4a200393f4a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"135\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38316249f1f1ad0f97ad5e11aa456202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97472a71daf37ee425da05a9a35a8cfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"130\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ee692f6dd791ff01a2892584fb69fb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4def91b5aa124408f0b91c7c9867b0e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#120;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3fcabe95fed981b55855f17301e42b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"155\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-62fc10e92b5ba7e95ba0c4173bc11cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf129d8eac2fcb3c302f27b77a6895ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f44e3fec8393a23a88132a3e4b686b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166497276654\">Solve Equations with Decimal Coefficients<\/h2>\n<p id=\"eip-497\">In the following exercises, solve the equation by clearing the decimals.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f43fec61543927a0979d31afc141352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;&#121;&#43;&#51;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac89e649f30b277ab2547e54977595fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;&#121;&#45;&#52;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23e1c2b0158308000bded0bf50e490d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#54;&#106;&#45;&#50;&#61;&#53;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90066b30e52ad1ffb488258c1bff3bcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#49;&#107;&#43;&#51;&#61;&#55;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"109\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a66cd2298c95ab63dcdcec86eeffb4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;&#120;&#43;&#48;&#46;&#54;&#61;&#48;&#46;&#53;&#120;&#45;&#49;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"177\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d88a8ab7ad9ebb20b39dfffa46662625_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;&#120;&#43;&#48;&#46;&#52;&#61;&#48;&#46;&#54;&#120;&#43;&#50;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"178\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d96db90ea2c0b0c90d16310d38d877b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#51;&#120;&#43;&#49;&#46;&#52;&#55;&#61;&#48;&#46;&#51;&#55;&#120;&#45;&#49;&#46;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"213\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81c1da2be9c0facbb52208dc99efb19c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;&#56;&#120;&#43;&#49;&#46;&#53;&#54;&#61;&#48;&#46;&#53;&#56;&#120;&#45;&#48;&#46;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"214\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47e75602511d99351865331e3c3996a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#57;&#120;&#45;&#49;&#46;&#50;&#53;&#61;&#48;&#46;&#55;&#53;&#120;&#43;&#49;&#46;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"204\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2eba473e4ce60e4e8ebd4b376e0271d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;&#120;&#45;&#48;&#46;&#57;&#49;&#61;&#48;&#46;&#56;&#120;&#43;&#50;&#46;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"195\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-810f5d059cc83f7f539c94d640861efb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#110;&#43;&#48;&#46;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#46;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"208\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-830593ccc0fef21cc2a8ae490fc0fe2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#110;&#43;&#48;&#46;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#46;&#53;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"208\" 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-1a5fafd19795dcbf31d03f586035d884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#48;&#100;&#43;&#48;&#46;&#50;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#100;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#46;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"205\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-28b3aa6a0e5cbe797df54a0572488234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#48;&#100;&#43;&#48;&#46;&#50;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#100;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#46;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"205\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0051be35ba0a4ace0538e44e6e1d36ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#48;&#46;&#50;&#53;&#113;&#61;&#51;&#46;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"204\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f831096d378281788c79b705e60bea0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#48;&#46;&#50;&#53;&#113;&#61;&#52;&#46;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"205\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div 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\">Coins<\/strong>\u00a0 41. Taylor has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcc081c0b035bbafb1bec51fa53c9087_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#50;&#46;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -1px;\" \/> in dimes and pennies. The number of pennies is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> more than the number of dimes. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9b9a091e83e564e9c68ede54ec53ea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#48;&#100;&#43;&#48;&#46;&#48;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#100;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"182\" style=\"vertical-align: -4px;\" \/> for <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;\" \/>, the number of dimes.<\/td>\n<td><strong data-effect=\"bold\">Stamps 42.\u00a0<\/strong> Travis bought <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a18b166b28de2529f6f51f872d52ed2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#57;&#46;&#52;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> worth of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1b97ea10a338260f21ee84c54901380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#57;&#45;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/> stamps and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-198bf5b86a401b3e2eed248932fe400c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#45;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/> stamps. The number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-198bf5b86a401b3e2eed248932fe400c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#45;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/> stamps was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than the number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1b97ea10a338260f21ee84c54901380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#57;&#45;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/> stamps. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d9e2e25f69e4ab1f71971f01b3b0617_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;&#57;&#115;&#43;&#48;&#46;&#50;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#57;&#46;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"203\" style=\"vertical-align: -4px;\" \/> for <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;\" \/>, to find the number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1b97ea10a338260f21ee84c54901380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#57;&#45;&#99;&#101;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/> stamps Travis bought.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table>\n<tbody>\n<tr>\n<td>43. Explain how to find the least common denominator of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a9f1e017f7f807913244b82f1a82527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#44;&#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;&#49;&#125;&#123;&#54;&#125;&#44;&#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;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#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;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"83\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td>44. If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?<\/td>\n<\/tr>\n<tr>\n<td>45. If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?<\/td>\n<td>46. In the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-280307ae58e18c62ac3cab38c1ddff57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#53;&#120;&#43;&#50;&#46;&#49;&#61;&#51;&#46;&#56;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"141\" style=\"vertical-align: -2px;\" \/>, what is the LCD? How do you know?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h1>Answers<\/h1>\n<\/div>\n<div data-depth=\"1\">\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. x = -1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. y = -1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f9d2e3abea9a3f3ae5ab7b620ec653c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. x = 4<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. m = 20<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. x = -3<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51d9906e6bc19d8bb463b525233b4a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. x = 1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. b = 12<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. x = 1<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. p = -41<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4bbe1878177bfeeef0086a1141568be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. y = 10<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. j = 2<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. x = 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. x = 18<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. x = 20<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. n = 9<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. d = 8<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. q = 11<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41 d = 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45.Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSolve Equations with Fraction or Decimal Coefficients\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1126","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1126","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\/1126\/revisions"}],"predecessor-version":[{"id":1127,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1126\/revisions\/1127"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1126\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1126"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1126"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1126"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}