{"id":16108,"date":"2019-10-01T17:41:05","date_gmt":"2019-10-01T17:41:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/expressions-and-equations\/"},"modified":"2020-10-22T09:07:26","modified_gmt":"2020-10-22T09:07:26","slug":"expressions-and-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/expressions-and-equations\/","title":{"raw":"7.1.c - Simplifying Equations Before Solving","rendered":"7.1.c &#8211; Simplifying Equations Before Solving"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve equations that need to be simplified<\/li>\r\n<\/ul>\r\n<\/div>\r\n\r\n[caption id=\"attachment_4415\" align=\"aligncenter\" width=\"300\"]<img class=\"size-medium wp-image-4415\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/05\/27201357\/Screen-Shot-2016-05-27-at-1.13.50-PM-300x296.png\" alt=\"steps leading to a gold ball\" width=\"300\" height=\"296\" \/> Steps With an End In Sight[\/caption]\r\n<h2>Use properties of equality to isolate variables and solve algebraic equations<\/h2>\r\nThere are some <b>equations<\/b> that you can solve in your head quickly. For example, what is the value of \u00a0[latex]y[\/latex] in the equation [latex]2y=6[\/latex]? Chances are you didn\u2019t need to get out a pencil and paper to calculate that [latex]y=3[\/latex]. You only needed to do one thing to get the answer: divide [latex]6[\/latex] by [latex]2[\/latex].\r\n\r\nOther equations are more complicated. \u00a0Although multi-step equations take more time and more operations to solve, they can still be simplified and solved by applying basic algebraic rules.\u00a0 In this section, we will look at equations that require some additional steps before they can be solved.\r\n<h3>Combining Like Terms<\/h3>\r\nMany equations start out more complicated than the ones we\u2019ve just solved in the previous section. Let's work through some examples that will employ simplifying by combining like terms.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]8x+9x - 5x=-3+15[\/latex]\r\n\r\nSolution:\r\n\r\nFirst, we need to simplify both sides of the equation as much as possible.\r\n\r\nStart by combining like terms to simplify each side.\r\n<table id=\"eip-id1168466098204\" class=\"unnumbered unstyled\" summary=\"The first line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]8x+9x-5x=-3+15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]12x=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by 12 to isolate x.<\/td>\r\n<td>[latex]\\Large\\frac{12x}{\\color{red}{12}}\\normalsize =\\Large\\frac{12}{\\color{red}{12}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Let [latex]x=1[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8x+9x-5x=-3+15[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8\\cdot\\color{red}{1}+9\\cdot\\color{red}{1}-5\\cdot\\color{red}{1}\\stackrel{\\text{?}}{=}-3+15[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]8+9-5\\stackrel{\\text{?}}{=}-3+15[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]12=12\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3x+5x+4-x+7=88[\/latex]\r\n\r\n[reveal-answer q=\"455516\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"455516\"]\r\n\r\nThere are three \u201clike\u201d terms [latex]3x[\/latex], [latex]5x[\/latex],\u00a0and\u00a0[latex]\u2013x[\/latex]\u00a0involving a variable.\u00a0Combine these \u201clike\u201d terms. [latex]4[\/latex] and [latex]7[\/latex] are also \u201clike\u201d terms and can be added.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+4+7=\\,\\,\\,88\\end{array}[\/latex]<\/p>\r\nThe equation is now in the form\u00a0[latex]ax+b=c[\/latex], so we can solve as before.\r\n<p style=\"text-align: center\">[latex]7x+11\\,\\,\\,=\\,\\,\\,88[\/latex]<\/p>\r\nSubtract \u00a0[latex]11[\/latex] from both sides.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}7x+11\\,\\,\\,=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{-11\\,\\,\\,\\,\\,\\,\\,-11}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x\\,\\,\\,=\\,\\,\\,77\\end{array}[\/latex]<\/p>\r\nDivide both sides by [latex]7[\/latex].\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{7x}\\,\\,\\,=\\,\\,\\,\\underline{77}\\\\7\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,=\\,\\,\\,11\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=11[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nHere is a similar problem for you to try.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141884&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\nIn the following video, we show an example of solving a linear equation that requires combining \u201clike\u201d terms.\r\n\r\nhttps:\/\/youtu.be\/ez_sP2OTGjU\r\n<h3>Solving equations when the variables are on the right side of the equation<\/h3>\r\nYou may not always have the variables on the left side of the equation, so we will show an example with variables on the right side. You will see that the properties used to solve this equation are exactly the same as the previous example.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [latex]11 - 20=17y - 8y - 6y[\/latex]\r\n\r\n[reveal-answer q=\"399092\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"399092\"]\r\n\r\nSolution:\r\n\r\nSimplify each side by combining like terms.\r\n<table id=\"eip-id1168466111452\" class=\"unnumbered unstyled\" summary=\"The first line shows 11 minus 20 equals 17y minus 8y minus 6y. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]11-20=17y-8y-6y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify each side.<\/td>\r\n<td>[latex]-9=3y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by 3 to isolate y.<\/td>\r\n<td>[latex]\\Large\\frac{-9}{\\color{red}{3}}\\normalsize =\\Large\\frac{3y}{\\color{red}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-3=y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Let [latex]y=-3[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11-20=17y-8y-6y[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11-20\\stackrel{\\text{?}}{=}17(\r\n\\color{red}{-3})-8(\\color{red}{-3})-6(\\color{red}{-3})[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11-20\\stackrel{\\text{?}}{=}-51+24+18[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-9=-9\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.\r\n\r\nNow you can try solving a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141901&amp;theme=oea&amp;iframe_resize_id=mom23[\/embed]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/qe89pkRKzRw\r\n<h3>Solving equations when the variables are on both sides of the equation<\/h3>\r\nYou may have noticed that in all the equations we have solved so far, we had\u00a0variables on only one\u00a0side of the equation. This does not happen all the time\u2014so now we\u2019ll see how to solve equations where there are variable terms on both sides of the equation, as in this equation: [latex]4x-6=2x+10[\/latex]. We will start like we did above\u2014choosing a variable side and a constant side, and then use the Subtraction and Addition Properties of Equality to collect all variables on one side and all constants on the other side. Remember, what you do to the left side of the equation, you must do to the right side as well.\r\n\r\nTo solve [latex]4x-6=2x+10[\/latex], we need to \u201cmove\u201d one of the variable terms.\u00a0This can make it difficult to decide which side to work with. It doesn\u2019t matter which term gets moved, [latex]4x[\/latex] or [latex]2x[\/latex], however, to avoid negative coefficients, you can move the smaller term.\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nSolve:\u00a0[latex]4x-6=2x+10[\/latex]\r\n\r\n[reveal-answer q=\"457216\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"457216\"]\r\n\r\nChoose the variable term to move\u2014to avoid negative terms choose [latex]2x[\/latex]\r\n<p style=\"text-align: center\">[latex]\\,\\,\\,4x-6=2x+10\\\\\\underline{-2x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-2x}\\\\\\,\\,\\,2x-6=10[\/latex]<\/p>\r\n<p style=\"text-align: left\">Now add\u00a06 to both\u00a0sides to isolate the term with the variable.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\2x=16\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">Now divide each side by [latex]2[\/latex] to isolate the variable [latex]x[\/latex].<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{2x}{2}=\\frac{16}{2}\\\\\\\\x=8\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn this video, we show an example of solving equations that have variables on both sides of the equal sign.\r\n\r\nhttps:\/\/youtu.be\/f3ujWNPL0Bw\r\n\r\n&nbsp;\r\n\r\nIn the next example,\u00a0the variable, [latex]x[\/latex], is on both sides, but the constants appear only on the right side, so we'll make the right side the \"constant\" side. Then the left side will be the \"variable\" side.\r\n<div class=\"textbox exercises\">\r\n<h3>ExampleS<\/h3>\r\nSolve: [latex]5x=4x+7[\/latex]\r\n[reveal-answer q=\"235739\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"235739\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168465095460\" class=\"unnumbered unstyled\" summary=\"The first line says 5x equals 4x plus 7. The left side is labeled \">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\">[latex]5x[\/latex] is the side containing only a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]4x+7[\/latex] is the side containing a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">We don't want any variables on the right, so subtract the [latex]4x[\/latex] .<\/td>\r\n<td>[latex]5x\\color{red}{-4x}=4x\\color{red}{-4x}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]x=7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">We have all the variables on one side and the constants on the other. We have solved the equation.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td><\/td>\r\n<td>[latex]5x=4x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]7[\/latex] for [latex]x[\/latex] .<\/td>\r\n<td><\/td>\r\n<td>[latex]5(\\color{red}{7})\\stackrel{\\text{?}}{=}4(\\color{red}{7})+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]35\\stackrel{\\text{?}}{=}28+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]35=35\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\nSolve: [latex]7x=-x+24[\/latex].\r\n[reveal-answer q=\"192799\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"192799\"]\r\n\r\nSolution:\r\nThe only constant, [latex]24[\/latex], is on the right, so let the left side be the variable side.\r\n<table id=\"eip-id1168467377760\" class=\"unnumbered unstyled\" summary=\"The first line says 7x equals negative x plus 24. The left side is labeled \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]7x[\/latex] is the side containing only a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]-x+24[\/latex] is the side containing a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove the [latex]-x[\/latex] from the right side by adding [latex]x[\/latex] to both sides.<\/td>\r\n<td>[latex]7x\\color{red}{+x}=-x\\color{red}{+x}+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]8x=24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>All the variables are on the left and the constants are on the right. Divide both sides by [latex]8[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{8x}{\\color{red}{8}}\\normalsize =\\Large\\frac{24}{\\color{red}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x=3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]7x=-x+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]x=3[\/latex].<\/td>\r\n<td>[latex]7(\\color{red}{3})\\stackrel{\\text{?}}{=}-(\\color{red}{3})+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]21=21\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nDid you see the subtle difference between the two equations? In the first, the right side looked like this: [latex]4x+7[\/latex], and in the second, the right side looked like this: [latex]-x+24[\/latex]. Even though they look different, we still used the same techniques to solve both.\r\n\r\nNow you can try solving an equation with variables on both sides, where it is beneficial to move the variable term to the left side.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142129&amp;theme=oea&amp;iframe_resize_id=mom3[\/embed]\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142132&amp;theme=oea&amp;iframe_resize_id=mom4[\/embed]\r\n\r\n<\/div>\r\nIn our last examples, we moved the variable term to the left side of the equation. In the next example, you will see that it is beneficial to move the variable term to the right side of the equation. There is no \"correct\" side to move the variable term, but the choice can help you avoid working with negative signs.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [latex]5y - 8=7y[\/latex]\r\n[reveal-answer q=\"100719\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"100719\"]\r\n\r\nSolution:\r\nThe only constant, [latex]-8[\/latex], is on the left side of the equation, and the variable, [latex]y[\/latex], is on both sides. Let\u2019s leave the constant on the left and collect the variables to the right.\r\n<table id=\"eip-id1168468768462\" class=\"unnumbered unstyled\" summary=\"The first line says 5y minus 8 equals 7y. The left side is labeled \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]5y-8[\/latex] is the side containing a <span style=\"color: #000000\"><span style=\"color: #ff0000\">constant<\/span>.<\/span><span style=\"color: #000000\">[latex]7y[\/latex] is the side containing only a <\/span><span style=\"color: #ff0000\">variable<\/span><span style=\"color: #000000\">.<\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract [latex]5y[\/latex] from both sides.<\/td>\r\n<td>[latex]5y\\color{red}{-5y}-8=7y\\color{red}{-5y}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-8=2y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We have the variables on the right and the constants on the left. Divide both sides by [latex]2[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{-8}{\\color{red}{2}}\\normalsize =\\Large\\frac{2y}{\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-4=y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with the variable on the left.<\/td>\r\n<td>[latex]y=-4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]5y-8=7y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Let [latex]y=-4[\/latex].<\/td>\r\n<td>[latex]5(\\color{red}{-4})-8\\stackrel{\\text{?}}{=}7(\\color{red}{-4})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-20-8\\stackrel{\\text{?}}{=}-28[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-28=-28\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try solving an equation where it is beneficial to move the variable term to the right side.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142125&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\n<h3>Solve Equations with Variables and Constants on Both Sides<\/h3>\r\nThe next example will be the first to have variables <em>and<\/em> constants on both sides of the equation. As we did before, we\u2019ll collect the variable terms to one side and the constants to the other side. You will see that as the number of variable and constant terms increases, so do the number of steps it takes to solve the equation.\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nSolve: [latex]7x+5=6x+2[\/latex]\r\n[reveal-answer q=\"859740\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"859740\"]\r\n\r\nSolution:\r\nStart by choosing which side will be the variable side and which side will be the constant side. The variable terms are [latex]7x[\/latex] and [latex]6x[\/latex]. Since [latex]7[\/latex] is greater than [latex]6[\/latex], make the left side the variable side, and so the right side will be the constant side.\r\n<table id=\"eip-id1168468709344\" class=\"unnumbered unstyled\" summary=\"The first line says 7x plus 5 equals 6x plus 2. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]7x+5=6x+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Collect the variable terms to the left side by subtracting [latex]6x[\/latex] from both sides.<\/td>\r\n<td>[latex]7x\\color{red}{-6x}+5=6x\\color{red}{-6x}+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x+5=2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now, collect the constants to the right side by subtracting [latex]5[\/latex] from both sides.<\/td>\r\n<td>[latex]x+5\\color{red}{-5}=2\\color{red}{-5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x=-3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The solution is [latex]x=-3[\/latex] .<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]7x+5=6x+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Let [latex]x=-3[\/latex].<\/td>\r\n<td>[latex]7(\\color{red}{-3})+5\\stackrel{\\text{?}}{=}6(\\color{red}{-3})+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-21+5\\stackrel{\\text{?}}{=}-18+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]16=16\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\nSolve: [latex]6n - 2=-3n+7[\/latex]\r\n\r\n[reveal-answer q=\"399032\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"399032\"]\r\nWe have [latex]6n[\/latex] on the left and [latex]-3n[\/latex] on the right. Since [latex]6&gt;-3[\/latex], make the left side the \"variable\" side.\r\n<table id=\"eip-id1168467335489\" class=\"unnumbered unstyled\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]6n-2=-3n+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We don't want variables on the right side\u2014add [latex]3n[\/latex] to both sides to leave only constants on the right.<\/td>\r\n<td>[latex]6n\\color{red}{+3n}-2=-3n\\color{red}{+3n}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]9n-2=7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We don't want any constants on the left side, so add [latex]2[\/latex] to both sides.<\/td>\r\n<td>[latex]9n-2\\color{red}{+2}=7\\color{red}{+2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]9n=9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The variable term is on the left and the constant term is on the right. To get the coefficient of [latex]n[\/latex] to be one, divide both sides by [latex]9[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{9n}{\\color{red}{9}}\\normalsize =\\Large\\frac{9}{\\color{red}{9}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]n=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]6n-2=-3n+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]1[\/latex] for [latex]n[\/latex].<\/td>\r\n<td>[latex]6(\\color{red}{1})-2\\stackrel{\\text{?}}{=}-3(\\color{red}{1})+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4=4\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video we show an example of how to solve a multi-step equation by moving the variable terms to one side and the constants to the other side. You will see that it doesn't matter which side you choose to be the variable side; you can get the correct answer either way.\r\n\r\nhttps:\/\/youtu.be\/_hBoWoctfAo\r\n\r\nIn the next example, we move the variable terms to the right side, to keep a positive coefficient on the variable.\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nSolve: [latex]2a - 7=5a+8[\/latex]\r\n\r\n[reveal-answer q=\"654456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"654456\"]\r\n\r\nSolution:\r\n\r\nThis equation has [latex]2a[\/latex] on the left and [latex]5a[\/latex] on the right. Since [latex]5&gt;2[\/latex], make the right side the variable side and the left side the constant side.\r\n<table id=\"eip-id1168466004451\" class=\"unnumbered unstyled\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2a-7=5a+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract [latex]2a[\/latex] from both sides to remove the variable term from the left.<\/td>\r\n<td>[latex]2a\\color{red}{-2a}-7=5a\\color{red}{-2a}+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]-7=3a+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract [latex]8[\/latex] from both sides to remove the constant from the right.<\/td>\r\n<td>[latex]-7\\color{red}{-8}=3a+8\\color{red}{-8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-15=3a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]3[\/latex] to make [latex]1[\/latex] the coefficient of [latex]a[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{-15}{\\color{red}{3}}\\normalsize =\\Large\\frac{3a}{\\color{red}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-5=a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]2a-7=5a+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Let [latex]a=-5[\/latex]<\/td>\r\n<td>[latex]2(\\color{red}{-5})-7\\stackrel{\\text{?}}{=}5(\\color{red}{-5})+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-10-7\\stackrel{\\text{?}}{=}-25+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-17=-17\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video shows another example of solving a multi-step\u00a0equation by moving the variable terms to one side and the constants to the other side.\r\n\r\nhttps:\/\/youtu.be\/kiYPW6hrTS4\r\n\r\nTry these problems to see how well you understand how to solve linear equations with variables and constants on both sides of the equal sign.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142134&amp;theme=oea&amp;iframe_resize_id=mom20[\/embed]\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142136&amp;theme=oea&amp;iframe_resize_id=mom200[\/embed]\r\n\r\n<\/div>\r\nWe just showed a lot of examples of different kinds of linear equations you may encounter. There are some good habits to develop that will help you solve all kinds of linear equations. We\u2019ll summarize the steps we took so you can easily refer to them.\r\n<div class=\"textbox shaded\">\r\n<h3>Solve an equation with variables and constants on both sides<\/h3>\r\n<ol id=\"eip-id1168468371331\" class=\"stepwise\">\r\n \t<li>Choose one side to be the variable side, and then the other will be the constant side.<\/li>\r\n \t<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Make the coefficient of the variable [latex]1[\/latex], using the Multiplication or Division Property of Equality.<\/li>\r\n \t<li>Check the solution by substituting it into the original equation.<\/li>\r\n<\/ol>\r\n<\/div>\r\nIn the next section, we will look at how to solve equations with parentheses by using the Distribution Property.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve equations that need to be simplified<\/li>\n<\/ul>\n<\/div>\n<div id=\"attachment_4415\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4415\" class=\"size-medium wp-image-4415\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/05\/27201357\/Screen-Shot-2016-05-27-at-1.13.50-PM-300x296.png\" alt=\"steps leading to a gold ball\" width=\"300\" height=\"296\" \/><\/p>\n<p id=\"caption-attachment-4415\" class=\"wp-caption-text\">Steps With an End In Sight<\/p>\n<\/div>\n<h2>Use properties of equality to isolate variables and solve algebraic equations<\/h2>\n<p>There are some <b>equations<\/b> that you can solve in your head quickly. For example, what is the value of \u00a0[latex]y[\/latex] in the equation [latex]2y=6[\/latex]? Chances are you didn\u2019t need to get out a pencil and paper to calculate that [latex]y=3[\/latex]. You only needed to do one thing to get the answer: divide [latex]6[\/latex] by [latex]2[\/latex].<\/p>\n<p>Other equations are more complicated. \u00a0Although multi-step equations take more time and more operations to solve, they can still be simplified and solved by applying basic algebraic rules.\u00a0 In this section, we will look at equations that require some additional steps before they can be solved.<\/p>\n<h3>Combining Like Terms<\/h3>\n<p>Many equations start out more complicated than the ones we\u2019ve just solved in the previous section. Let&#8217;s work through some examples that will employ simplifying by combining like terms.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]8x+9x - 5x=-3+15[\/latex]<\/p>\n<p>Solution:<\/p>\n<p>First, we need to simplify both sides of the equation as much as possible.<\/p>\n<p>Start by combining like terms to simplify each side.<\/p>\n<table id=\"eip-id1168466098204\" class=\"unnumbered unstyled\" summary=\"The first line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]8x+9x-5x=-3+15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]12x=12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 12 to isolate x.<\/td>\n<td>[latex]\\Large\\frac{12x}{\\color{red}{12}}\\normalsize =\\Large\\frac{12}{\\color{red}{12}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let [latex]x=1[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]8x+9x-5x=-3+15[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]8\\cdot\\color{red}{1}+9\\cdot\\color{red}{1}-5\\cdot\\color{red}{1}\\stackrel{\\text{?}}{=}-3+15[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]8+9-5\\stackrel{\\text{?}}{=}-3+15[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]12=12\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3x+5x+4-x+7=88[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q455516\">Show Solution<\/span><\/p>\n<div id=\"q455516\" class=\"hidden-answer\" style=\"display: none\">\n<p>There are three \u201clike\u201d terms [latex]3x[\/latex], [latex]5x[\/latex],\u00a0and\u00a0[latex]\u2013x[\/latex]\u00a0involving a variable.\u00a0Combine these \u201clike\u201d terms. [latex]4[\/latex] and [latex]7[\/latex] are also \u201clike\u201d terms and can be added.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+4+7=\\,\\,\\,88\\end{array}[\/latex]<\/p>\n<p>The equation is now in the form\u00a0[latex]ax+b=c[\/latex], so we can solve as before.<\/p>\n<p style=\"text-align: center\">[latex]7x+11\\,\\,\\,=\\,\\,\\,88[\/latex]<\/p>\n<p>Subtract \u00a0[latex]11[\/latex] from both sides.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}7x+11\\,\\,\\,=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{-11\\,\\,\\,\\,\\,\\,\\,-11}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x\\,\\,\\,=\\,\\,\\,77\\end{array}[\/latex]<\/p>\n<p>Divide both sides by [latex]7[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{7x}\\,\\,\\,=\\,\\,\\,\\underline{77}\\\\7\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,=\\,\\,\\,11\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=11[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>Here is a similar problem for you to try.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141884\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141884&#38;theme=oea&#38;iframe_resize_id=ohm141884&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video, we show an example of solving a linear equation that requires combining \u201clike\u201d terms.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solving an Equation that Requires Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ez_sP2OTGjU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Solving equations when the variables are on the right side of the equation<\/h3>\n<p>You may not always have the variables on the left side of the equation, so we will show an example with variables on the right side. You will see that the properties used to solve this equation are exactly the same as the previous example.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]11 - 20=17y - 8y - 6y[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q399092\">Show Solution<\/span><\/p>\n<div id=\"q399092\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p>Simplify each side by combining like terms.<\/p>\n<table id=\"eip-id1168466111452\" class=\"unnumbered unstyled\" summary=\"The first line shows 11 minus 20 equals 17y minus 8y minus 6y. The next line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]11-20=17y-8y-6y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify each side.<\/td>\n<td>[latex]-9=3y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 3 to isolate y.<\/td>\n<td>[latex]\\Large\\frac{-9}{\\color{red}{3}}\\normalsize =\\Large\\frac{3y}{\\color{red}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-3=y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let [latex]y=-3[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]11-20=17y-8y-6y[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]11-20\\stackrel{\\text{?}}{=}17(  \\color{red}{-3})-8(\\color{red}{-3})-6(\\color{red}{-3})[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]11-20\\stackrel{\\text{?}}{=}-51+24+18[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]-9=-9\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.<\/p>\n<p>Now you can try solving a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141901\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141901&#38;theme=oea&#38;iframe_resize_id=ohm141901&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Solve Linear Equations in One Variable with Simplifying (One-Step Mult\/Div)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qe89pkRKzRw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Solving equations when the variables are on both sides of the equation<\/h3>\n<p>You may have noticed that in all the equations we have solved so far, we had\u00a0variables on only one\u00a0side of the equation. This does not happen all the time\u2014so now we\u2019ll see how to solve equations where there are variable terms on both sides of the equation, as in this equation: [latex]4x-6=2x+10[\/latex]. We will start like we did above\u2014choosing a variable side and a constant side, and then use the Subtraction and Addition Properties of Equality to collect all variables on one side and all constants on the other side. Remember, what you do to the left side of the equation, you must do to the right side as well.<\/p>\n<p>To solve [latex]4x-6=2x+10[\/latex], we need to \u201cmove\u201d one of the variable terms.\u00a0This can make it difficult to decide which side to work with. It doesn\u2019t matter which term gets moved, [latex]4x[\/latex] or [latex]2x[\/latex], however, to avoid negative coefficients, you can move the smaller term.<\/p>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>Solve:\u00a0[latex]4x-6=2x+10[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q457216\">Show Solution<\/span><\/p>\n<div id=\"q457216\" class=\"hidden-answer\" style=\"display: none\">\n<p>Choose the variable term to move\u2014to avoid negative terms choose [latex]2x[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\,\\,\\,4x-6=2x+10\\\\\\underline{-2x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-2x}\\\\\\,\\,\\,2x-6=10[\/latex]<\/p>\n<p style=\"text-align: left\">Now add\u00a06 to both\u00a0sides to isolate the term with the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\2x=16\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">Now divide each side by [latex]2[\/latex] to isolate the variable [latex]x[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{2x}{2}=\\frac{16}{2}\\\\\\\\x=8\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In this video, we show an example of solving equations that have variables on both sides of the equal sign.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Solve an Equation with Variable on Both Sides\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/f3ujWNPL0Bw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>In the next example,\u00a0the variable, [latex]x[\/latex], is on both sides, but the constants appear only on the right side, so we&#8217;ll make the right side the &#8220;constant&#8221; side. Then the left side will be the &#8220;variable&#8221; side.<\/p>\n<div class=\"textbox exercises\">\n<h3>ExampleS<\/h3>\n<p>Solve: [latex]5x=4x+7[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q235739\">Show Solution<\/span><\/p>\n<div id=\"q235739\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168465095460\" class=\"unnumbered unstyled\" summary=\"The first line says 5x equals 4x plus 7. The left side is labeled\">\n<tbody>\n<tr>\n<td colspan=\"2\">[latex]5x[\/latex] is the side containing only a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]4x+7[\/latex] is the side containing a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We don&#8217;t want any variables on the right, so subtract the [latex]4x[\/latex] .<\/td>\n<td>[latex]5x\\color{red}{-4x}=4x\\color{red}{-4x}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]x=7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">We have all the variables on one side and the constants on the other. We have solved the equation.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><\/td>\n<td>[latex]5x=4x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]7[\/latex] for [latex]x[\/latex] .<\/td>\n<td><\/td>\n<td>[latex]5(\\color{red}{7})\\stackrel{\\text{?}}{=}4(\\color{red}{7})+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]35\\stackrel{\\text{?}}{=}28+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]35=35\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>Solve: [latex]7x=-x+24[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q192799\">Show Solution<\/span><\/p>\n<div id=\"q192799\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe only constant, [latex]24[\/latex], is on the right, so let the left side be the variable side.<\/p>\n<table id=\"eip-id1168467377760\" class=\"unnumbered unstyled\" summary=\"The first line says 7x equals negative x plus 24. The left side is labeled\">\n<tbody>\n<tr>\n<td>[latex]7x[\/latex] is the side containing only a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]-x+24[\/latex] is the side containing a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Remove the [latex]-x[\/latex] from the right side by adding [latex]x[\/latex] to both sides.<\/td>\n<td>[latex]7x\\color{red}{+x}=-x\\color{red}{+x}+24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]8x=24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>All the variables are on the left and the constants are on the right. Divide both sides by [latex]8[\/latex].<\/td>\n<td>[latex]\\Large\\frac{8x}{\\color{red}{8}}\\normalsize =\\Large\\frac{24}{\\color{red}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x=3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]7x=-x+24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]x=3[\/latex].<\/td>\n<td>[latex]7(\\color{red}{3})\\stackrel{\\text{?}}{=}-(\\color{red}{3})+24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]21=21\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Did you see the subtle difference between the two equations? In the first, the right side looked like this: [latex]4x+7[\/latex], and in the second, the right side looked like this: [latex]-x+24[\/latex]. Even though they look different, we still used the same techniques to solve both.<\/p>\n<p>Now you can try solving an equation with variables on both sides, where it is beneficial to move the variable term to the left side.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142129\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142129&#38;theme=oea&#38;iframe_resize_id=ohm142129&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142132\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142132&#38;theme=oea&#38;iframe_resize_id=ohm142132&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In our last examples, we moved the variable term to the left side of the equation. In the next example, you will see that it is beneficial to move the variable term to the right side of the equation. There is no &#8220;correct&#8221; side to move the variable term, but the choice can help you avoid working with negative signs.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]5y - 8=7y[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q100719\">Show Solution<\/span><\/p>\n<div id=\"q100719\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe only constant, [latex]-8[\/latex], is on the left side of the equation, and the variable, [latex]y[\/latex], is on both sides. Let\u2019s leave the constant on the left and collect the variables to the right.<\/p>\n<table id=\"eip-id1168468768462\" class=\"unnumbered unstyled\" summary=\"The first line says 5y minus 8 equals 7y. The left side is labeled\">\n<tbody>\n<tr>\n<td>[latex]5y-8[\/latex] is the side containing a <span style=\"color: #000000\"><span style=\"color: #ff0000\">constant<\/span>.<\/span><span style=\"color: #000000\">[latex]7y[\/latex] is the side containing only a <\/span><span style=\"color: #ff0000\">variable<\/span><span style=\"color: #000000\">.<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Subtract [latex]5y[\/latex] from both sides.<\/td>\n<td>[latex]5y\\color{red}{-5y}-8=7y\\color{red}{-5y}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-8=2y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We have the variables on the right and the constants on the left. Divide both sides by [latex]2[\/latex].<\/td>\n<td>[latex]\\Large\\frac{-8}{\\color{red}{2}}\\normalsize =\\Large\\frac{2y}{\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-4=y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the variable on the left.<\/td>\n<td>[latex]y=-4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]5y-8=7y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Let [latex]y=-4[\/latex].<\/td>\n<td>[latex]5(\\color{red}{-4})-8\\stackrel{\\text{?}}{=}7(\\color{red}{-4})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-20-8\\stackrel{\\text{?}}{=}-28[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-28=-28\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try solving an equation where it is beneficial to move the variable term to the right side.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142125\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142125&#38;theme=oea&#38;iframe_resize_id=ohm142125&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Solve Equations with Variables and Constants on Both Sides<\/h3>\n<p>The next example will be the first to have variables <em>and<\/em> constants on both sides of the equation. As we did before, we\u2019ll collect the variable terms to one side and the constants to the other side. You will see that as the number of variable and constant terms increases, so do the number of steps it takes to solve the equation.<\/p>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>Solve: [latex]7x+5=6x+2[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q859740\">Show Solution<\/span><\/p>\n<div id=\"q859740\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nStart by choosing which side will be the variable side and which side will be the constant side. The variable terms are [latex]7x[\/latex] and [latex]6x[\/latex]. Since [latex]7[\/latex] is greater than [latex]6[\/latex], make the left side the variable side, and so the right side will be the constant side.<\/p>\n<table id=\"eip-id1168468709344\" class=\"unnumbered unstyled\" summary=\"The first line says 7x plus 5 equals 6x plus 2. The next line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]7x+5=6x+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Collect the variable terms to the left side by subtracting [latex]6x[\/latex] from both sides.<\/td>\n<td>[latex]7x\\color{red}{-6x}+5=6x\\color{red}{-6x}+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x+5=2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Now, collect the constants to the right side by subtracting [latex]5[\/latex] from both sides.<\/td>\n<td>[latex]x+5\\color{red}{-5}=2\\color{red}{-5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x=-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The solution is [latex]x=-3[\/latex] .<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]7x+5=6x+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Let [latex]x=-3[\/latex].<\/td>\n<td>[latex]7(\\color{red}{-3})+5\\stackrel{\\text{?}}{=}6(\\color{red}{-3})+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-21+5\\stackrel{\\text{?}}{=}-18+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]16=16\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>Solve: [latex]6n - 2=-3n+7[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q399032\">Show Solution<\/span><\/p>\n<div id=\"q399032\" class=\"hidden-answer\" style=\"display: none\">\nWe have [latex]6n[\/latex] on the left and [latex]-3n[\/latex] on the right. Since [latex]6>-3[\/latex], make the left side the &#8220;variable&#8221; side.<\/p>\n<table id=\"eip-id1168467335489\" class=\"unnumbered unstyled\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]6n-2=-3n+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We don&#8217;t want variables on the right side\u2014add [latex]3n[\/latex] to both sides to leave only constants on the right.<\/td>\n<td>[latex]6n\\color{red}{+3n}-2=-3n\\color{red}{+3n}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]9n-2=7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We don&#8217;t want any constants on the left side, so add [latex]2[\/latex] to both sides.<\/td>\n<td>[latex]9n-2\\color{red}{+2}=7\\color{red}{+2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]9n=9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The variable term is on the left and the constant term is on the right. To get the coefficient of [latex]n[\/latex] to be one, divide both sides by [latex]9[\/latex].<\/td>\n<td>[latex]\\Large\\frac{9n}{\\color{red}{9}}\\normalsize =\\Large\\frac{9}{\\color{red}{9}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]n=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]6n-2=-3n+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]1[\/latex] for [latex]n[\/latex].<\/td>\n<td>[latex]6(\\color{red}{1})-2\\stackrel{\\text{?}}{=}-3(\\color{red}{1})+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]4=4\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video we show an example of how to solve a multi-step equation by moving the variable terms to one side and the constants to the other side. You will see that it doesn&#8217;t matter which side you choose to be the variable side; you can get the correct answer either way.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Solve a Linear Equation in One Variable with Variables on Both Sides: 2x+8=-2x-24\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_hBoWoctfAo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example, we move the variable terms to the right side, to keep a positive coefficient on the variable.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Solve: [latex]2a - 7=5a+8[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q654456\">Show Solution<\/span><\/p>\n<div id=\"q654456\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p>This equation has [latex]2a[\/latex] on the left and [latex]5a[\/latex] on the right. Since [latex]5>2[\/latex], make the right side the variable side and the left side the constant side.<\/p>\n<table id=\"eip-id1168466004451\" class=\"unnumbered unstyled\" summary=\"The top line says 6n minus 2 equals negative 3n plus 7. The next line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2a-7=5a+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract [latex]2a[\/latex] from both sides to remove the variable term from the left.<\/td>\n<td>[latex]2a\\color{red}{-2a}-7=5a\\color{red}{-2a}+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]-7=3a+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract [latex]8[\/latex] from both sides to remove the constant from the right.<\/td>\n<td>[latex]-7\\color{red}{-8}=3a+8\\color{red}{-8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-15=3a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]3[\/latex] to make [latex]1[\/latex] the coefficient of [latex]a[\/latex] .<\/td>\n<td>[latex]\\Large\\frac{-15}{\\color{red}{3}}\\normalsize =\\Large\\frac{3a}{\\color{red}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-5=a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]2a-7=5a+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Let [latex]a=-5[\/latex]<\/td>\n<td>[latex]2(\\color{red}{-5})-7\\stackrel{\\text{?}}{=}5(\\color{red}{-5})+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-10-7\\stackrel{\\text{?}}{=}-25+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-17=-17\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video shows another example of solving a multi-step\u00a0equation by moving the variable terms to one side and the constants to the other side.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Solve a Linear Equation in One Variable with Variables on Both Sides: 2m-9=6m-17\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/kiYPW6hrTS4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Try these problems to see how well you understand how to solve linear equations with variables and constants on both sides of the equal sign.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142134\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142134&#38;theme=oea&#38;iframe_resize_id=ohm142134&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142136\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142136&#38;theme=oea&#38;iframe_resize_id=ohm142136&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>We just showed a lot of examples of different kinds of linear equations you may encounter. There are some good habits to develop that will help you solve all kinds of linear equations. We\u2019ll summarize the steps we took so you can easily refer to them.<\/p>\n<div class=\"textbox shaded\">\n<h3>Solve an equation with variables and constants on both sides<\/h3>\n<ol id=\"eip-id1168468371331\" class=\"stepwise\">\n<li>Choose one side to be the variable side, and then the other will be the constant side.<\/li>\n<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable [latex]1[\/latex], using the Multiplication or Division Property of Equality.<\/li>\n<li>Check the solution by substituting it into the original equation.<\/li>\n<\/ol>\n<\/div>\n<p>In the next section, we will look at how to solve equations with parentheses by using the Distribution Property.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-16108\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Image: Steps With an End In Sight. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solving Two Step Equations (Basic). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fCyxSVQKeRw\">https:\/\/youtu.be\/fCyxSVQKeRw<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solving an Equation that Requires Combining Like Terms. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ez_sP2OTGjU\">https:\/\/youtu.be\/ez_sP2OTGjU<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Solve an Equation with Variable on Both Sides. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/f3ujWNPL0Bw\">https:\/\/youtu.be\/f3ujWNPL0Bw<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex 4: Solving Absolute Value Equations (Requires Isolating Abs. Value). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/-HrOMkIiSfU\">https:\/\/youtu.be\/-HrOMkIiSfU<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex 5: Solving Absolute Value Equations (Requires Isolating Abs. Value). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/2bEA7HoDfpk\">https:\/\/youtu.be\/2bEA7HoDfpk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169554,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Image: Steps With an End In Sight\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solving Two Step Equations (Basic)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/fCyxSVQKeRw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solving an Equation that Requires Combining Like Terms\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ez_sP2OTGjU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Solve an Equation with Variable on Both Sides\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/f3ujWNPL0Bw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 4: Solving Absolute Value Equations (Requires Isolating Abs. 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