{"id":77,"date":"2023-06-21T13:22:30","date_gmt":"2023-06-21T13:22:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topic-1\/"},"modified":"2024-01-08T18:46:57","modified_gmt":"2024-01-08T18:46:57","slug":"review-topic-1","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/review-topic-1\/","title":{"raw":"R1.1   Multi-Step Equations","rendered":"R1.1   Multi-Step Equations"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use properties of equality to isolate variables and solve algebraic equations<\/li>\r\n \t<li>Solve equations containing absolute value<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Use Properties of Equality to Isolate Variables and Solve Algebraic Equations<\/h2>\r\n<div class=\"textbox examples\">\r\n<h3>Review terminology: expressions<\/h3>\r\nRecall that a mathematical <strong>expression<\/strong> consists of terms connected by addition or subtraction, each term of which consists of variables and numbers connected by multiplication or division.\r\n<ul>\r\n \t<li><strong>variables: <\/strong> variables are symbols that stand for an unknown quantity; they are often represented with letters, like <em>x, y, or z.<\/em><\/li>\r\n \t<li><strong>coefficient: <\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of \u00a0[latex]3x[\/latex] is [latex]3[\/latex].<\/li>\r\n \t<li><strong>term: <\/strong>a single number, or variables and numbers connected by multiplication. [latex]-4, 6x[\/latex] and [latex]x^2[\/latex] are all terms.<\/li>\r\n \t<li><strong>expression: <\/strong>groups of terms connected by addition and subtraction. [latex]2x^2-5[\/latex] is an expression.<\/li>\r\n<\/ul>\r\n<\/div>\r\nAn <strong>equation<\/strong> is a mathematical statement of the equivalency of two expressions.. An equation will always contain an equal sign with an expression on each side. Think of an equal sign as meaning \"the same as.\" Some examples of equations are [latex]y = mx +b[\/latex], [latex]\\Large\\frac{3}{4}\\normalsize r = v^{3} - r[\/latex], and [latex]2(6-d) + f(3 +k) =\\Large\\frac{1}{4}\\normalsize d[\/latex].\r\n\r\nThe following figure shows how coefficients, variables, terms, and expressions all come together to make equations. In the equation [latex]2x-3^2=10x[\/latex], the variable is [latex]x[\/latex], a coefficient is [latex]10[\/latex], a term is [latex]10x[\/latex], an expression is [latex]2x-3^2[\/latex].\r\n\r\n<img class=\"wp-image-4693 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/08214552\/Screen-Shot-2016-06-08-at-2.45.15-PM-300x242.png\" alt=\"Equation made of coefficients, variables, terms and expressions.\" width=\"424\" height=\"342\" \/>\r\n\r\nThere are some <b>equations<\/b> that you can solve in your head quickly. For example, what is the value of <i>y<\/i> 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. Solving [latex]\\displaystyle 4\\left(\\frac{1}{3}\\normalsize t+\\frac{1}{2}\\normalsize\\right)=6[\/latex] without writing anything down is difficult! That is because this equation contains not just a <b>variable<\/b> but also fractions and <b>terms<\/b> inside parentheses. This is a <b>multi-step equation,\u00a0<\/b>one that takes several steps to solve. Although multi-step equations take more time and more operations, they can still be simplified and solved by applying basic algebraic rules.\r\n\r\nRemember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The <b>addition property of equality<\/b> and the <b>multiplication property of equality<\/b> explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you will keep both sides of the equation equal.\r\n\r\nIf the equation is in the form [latex]ax+b=c[\/latex], where <i>x<\/i> is the variable, you can solve the equation as before. First \u201cundo\u201d the addition and subtraction and then \u201cundo\u201d the multiplication and division.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3y+2=11[\/latex].\r\n\r\n[reveal-answer q=\"843520\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"843520\"]\r\n\r\nSubtract 2 from both sides of the equation to get the term with the variable by itself.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{r}3y+2\\,\\,\\,=\\,\\,11\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,-2\\,\\,\\,\\,\\,\\,\\,\\,-2}\\\\3y\\,\\,\\,\\,=\\,\\,\\,\\,\\,9\\end{array}[\/latex]<\/p>\r\nDivide both sides of the equation by [latex]3[\/latex] to get a coefficient of [latex]1[\/latex] for the variable.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\underline{3y}\\,\\,\\,\\,=\\,\\,\\,\\,\\,\\underline{9}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,\\,\\,=\\,\\,\\,\\,3\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\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 like terms involving a variable: [latex]3x[\/latex], [latex]5x[\/latex], and [latex]\u2013x[\/latex]. Combine these like terms. [latex]4[\/latex] and [latex]7[\/latex] are also like terms and can be added.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+11=\\,\\,\\,88\\end{array}[\/latex]<\/p>\r\nThe equation is now in the form [latex]ax+b=c[\/latex], so we can solve as before.\r\n\r\nSubtract 11 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 7.\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[\/hidden-answer]\r\n\r\n<\/div>\r\nSome equations may have the variable on both sides of the equal sign, as in this equation: [latex]4x-6=2x+10[\/latex].\r\n\r\nTo solve this equation, we need to \u201cmove\u201d one of the variable terms. This can make it difficult to decide which side to work with. It does not 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: [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}\\\\\\,\\,\\,4x-6=10[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Now add 6 to both sides to isolate the term with the variable.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\2x=16\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Now divide each side by 2 to isolate the variable x.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\Large\\frac{2x}{2}\\normalsize=\\Large\\frac{16}{2}\\\\\\\\\\normalsize{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\n[embed]https:\/\/youtu.be\/f3ujWNPL0Bw[\/embed]\r\n<h2>Solving Multi-Step Equations With Absolute Value<\/h2>\r\nWe can apply the same techniques we used for solving a one-step equation which contained absolute value to an equation that will take more than one step to solve. Let us start with an example where the first step is to write two equations, one equal to positive [latex]26[\/latex] and one equal to negative [latex]26[\/latex].\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve for <i>p<\/i>. [latex]\\left|2p\u20134\\right|=26[\/latex]\r\n\r\n[reveal-answer q=\"371950\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"371950\"]\r\n\r\nWrite the two equations that will give an absolute value of [latex]26[\/latex].\r\n<p style=\"text-align: center;\">[latex] \\displaystyle 2p-4=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,2p-4=\\,-26[\/latex]<\/p>\r\nSolve each equation for <i>p <\/i>by isolating the variable<i>.<\/i>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{r}2p-4=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2p-4=\\,-26\\\\\\underline{\\,\\,\\,\\,\\,\\,+4\\,\\,\\,\\,+4}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{\\,\\,\\,\\,\\,\\,\\,+4\\,\\,\\,\\,\\,\\,\\,+4}\\\\\\underline{2p}\\,\\,\\,\\,\\,\\,=\\underline{30}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{2p}\\,\\,\\,\\,\\,=\\,\\underline{-22}\\\\2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,p=15\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,p=\\,-11\\end{array}[\/latex]<\/p>\r\nCheck the solutions in the original equation.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,\\left| 2p-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| 2p-4 \\right|=26\\\\\\left| 2(15)-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\left| 2(-11)-4 \\right|=26\\\\\\,\\,\\,\\,\\,\\left| 30-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| -22-4 \\right|=26\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| 26 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| -26 \\right|=26\\end{array}[\/latex]<\/p>\r\nBoth solutions check!\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next video, we show more examples of solving a simple absolute value equation.\r\n\r\nhttps:\/\/youtu.be\/4g-o_-mAFpc\r\n\r\nNow let us look at an example where you need to do an algebraic step or two before you can write your two equations. The goal here is to get the absolute value on one side of the equation by itself. Then we can proceed as we did in the previous example.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve for <i>w<\/i>. [latex]3\\left|4w\u20131\\right|\u20135=10[\/latex]\r\n\r\n[reveal-answer q=\"303228\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"303228\"]\r\n\r\nIsolate the term with the absolute value by adding 5 to both sides.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}3\\left|4w-1\\right|-5=10\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+5\\,\\,\\,+5}\\\\ 3\\left|4w-1\\right|=15\\end{array}[\/latex]<\/p>\r\nDivide both sides by 3. Now the absolute value is isolated.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r} \\underline{3\\left|4w-1\\right|}=\\underline{15}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\,\\,\\\\\\left|4w-1\\right|=\\,\\,5\\end{array}[\/latex]<\/p>\r\nWrite the two equations that will give an absolute value of 5 and solve them.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{r}4w-1=5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4w-1=-5\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,+1\\,\\,+1}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{\\,\\,\\,\\,\\,\\,\\,\\,\\,+1\\,\\,\\,\\,\\,+1}\\\\\\,\\,\\,\\,\\,\\underline{4w}=\\underline{6}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{4w}\\,\\,\\,\\,\\,\\,\\,=\\underline{-4}\\\\4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,w=\\Large\\frac{3}{2}\\normalsize \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,w=-1\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,w=\\Large\\frac{3}{2}\\normalsize \\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,-1\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nCheck the solutions in the original equation.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\\\\\\\3\\left| 4\\left(\\Large\\frac{3}{2}\\normalsize\\right)-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\\\\\\\\\,\\,\\,\\,\\,\\,3\\left|\\Large\\frac{12}{2}\\normalsize -1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,3\\left| 4(-1)-1\\, \\right|-5=10\\\\\\\\\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 6-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| -4-1\\, \\right|-5=10\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left(5\\right)-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| -5 \\right|-5=10\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,15-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,15-5=10\\\\10=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,10=10\\end{array}[\/latex]<\/p>\r\nBoth solutions check!\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the two videos that follow, we show examples of how to solve an absolute value equation that requires you to isolate the absolute value first using mathematical operations.\r\n\r\nhttps:\/\/youtu.be\/-HrOMkIiSfU\r\n\r\nhttps:\/\/youtu.be\/2bEA7HoDfpk","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use properties of equality to isolate variables and solve algebraic equations<\/li>\n<li>Solve equations containing absolute value<\/li>\n<\/ul>\n<\/div>\n<h2>Use Properties of Equality to Isolate Variables and Solve Algebraic Equations<\/h2>\n<div class=\"textbox examples\">\n<h3>Review terminology: expressions<\/h3>\n<p>Recall that a mathematical <strong>expression<\/strong> consists of terms connected by addition or subtraction, each term of which consists of variables and numbers connected by multiplication or division.<\/p>\n<ul>\n<li><strong>variables: <\/strong> variables are symbols that stand for an unknown quantity; they are often represented with letters, like <em>x, y, or z.<\/em><\/li>\n<li><strong>coefficient: <\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of \u00a0[latex]3x[\/latex] is [latex]3[\/latex].<\/li>\n<li><strong>term: <\/strong>a single number, or variables and numbers connected by multiplication. [latex]-4, 6x[\/latex] and [latex]x^2[\/latex] are all terms.<\/li>\n<li><strong>expression: <\/strong>groups of terms connected by addition and subtraction. [latex]2x^2-5[\/latex] is an expression.<\/li>\n<\/ul>\n<\/div>\n<p>An <strong>equation<\/strong> is a mathematical statement of the equivalency of two expressions.. An equation will always contain an equal sign with an expression on each side. Think of an equal sign as meaning &#8220;the same as.&#8221; Some examples of equations are [latex]y = mx +b[\/latex], [latex]\\Large\\frac{3}{4}\\normalsize r = v^{3} - r[\/latex], and [latex]2(6-d) + f(3 +k) =\\Large\\frac{1}{4}\\normalsize d[\/latex].<\/p>\n<p>The following figure shows how coefficients, variables, terms, and expressions all come together to make equations. In the equation [latex]2x-3^2=10x[\/latex], the variable is [latex]x[\/latex], a coefficient is [latex]10[\/latex], a term is [latex]10x[\/latex], an expression is [latex]2x-3^2[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4693 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/08214552\/Screen-Shot-2016-06-08-at-2.45.15-PM-300x242.png\" alt=\"Equation made of coefficients, variables, terms and expressions.\" width=\"424\" height=\"342\" \/><\/p>\n<p>There are some <b>equations<\/b> that you can solve in your head quickly. For example, what is the value of <i>y<\/i> 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. Solving [latex]\\displaystyle 4\\left(\\frac{1}{3}\\normalsize t+\\frac{1}{2}\\normalsize\\right)=6[\/latex] without writing anything down is difficult! That is because this equation contains not just a <b>variable<\/b> but also fractions and <b>terms<\/b> inside parentheses. This is a <b>multi-step equation,\u00a0<\/b>one that takes several steps to solve. Although multi-step equations take more time and more operations, they can still be simplified and solved by applying basic algebraic rules.<\/p>\n<p>Remember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The <b>addition property of equality<\/b> and the <b>multiplication property of equality<\/b> explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you will keep both sides of the equation equal.<\/p>\n<p>If the equation is in the form [latex]ax+b=c[\/latex], where <i>x<\/i> is the variable, you can solve the equation as before. First \u201cundo\u201d the addition and subtraction and then \u201cundo\u201d the multiplication and division.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3y+2=11[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q843520\">Show Solution<\/span><\/p>\n<div id=\"q843520\" class=\"hidden-answer\" style=\"display: none\">\n<p>Subtract 2 from both sides of the equation to get the term with the variable by itself.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{r}3y+2\\,\\,\\,=\\,\\,11\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,-2\\,\\,\\,\\,\\,\\,\\,\\,-2}\\\\3y\\,\\,\\,\\,=\\,\\,\\,\\,\\,9\\end{array}[\/latex]<\/p>\n<p>Divide both sides of the equation by [latex]3[\/latex] to get a coefficient of [latex]1[\/latex] for the variable.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\underline{3y}\\,\\,\\,\\,=\\,\\,\\,\\,\\,\\underline{9}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,\\,\\,=\\,\\,\\,\\,3\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\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 like terms involving a variable: [latex]3x[\/latex], [latex]5x[\/latex], and [latex]\u2013x[\/latex]. Combine these like terms. [latex]4[\/latex] and [latex]7[\/latex] are also like terms and can be added.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+11=\\,\\,\\,88\\end{array}[\/latex]<\/p>\n<p>The equation is now in the form [latex]ax+b=c[\/latex], so we can solve as before.<\/p>\n<p>Subtract 11 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 7.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{7x}\\,\\,\\,=\\,\\,\\,\\underline{77}\\\\7\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,=\\,\\,\\,11\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Some equations may have the variable on both sides of the equal sign, as in this equation: [latex]4x-6=2x+10[\/latex].<\/p>\n<p>To solve this equation, we need to \u201cmove\u201d one of the variable terms. This can make it difficult to decide which side to work with. It does not 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: [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}\\\\\\,\\,\\,4x-6=10[\/latex]<\/p>\n<p style=\"text-align: left;\">Now add 6 to both sides to isolate the term with the variable.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\2x=16\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left;\">Now divide each side by 2 to isolate the variable x.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\Large\\frac{2x}{2}\\normalsize=\\Large\\frac{16}{2}\\\\\\\\\\normalsize{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-1\" 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<h2>Solving Multi-Step Equations With Absolute Value<\/h2>\n<p>We can apply the same techniques we used for solving a one-step equation which contained absolute value to an equation that will take more than one step to solve. Let us start with an example where the first step is to write two equations, one equal to positive [latex]26[\/latex] and one equal to negative [latex]26[\/latex].<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve for <i>p<\/i>. [latex]\\left|2p\u20134\\right|=26[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q371950\">Show Solution<\/span><\/p>\n<div id=\"q371950\" class=\"hidden-answer\" style=\"display: none\">\n<p>Write the two equations that will give an absolute value of [latex]26[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle 2p-4=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,2p-4=\\,-26[\/latex]<\/p>\n<p>Solve each equation for <i>p <\/i>by isolating the variable<i>.<\/i><\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{r}2p-4=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2p-4=\\,-26\\\\\\underline{\\,\\,\\,\\,\\,\\,+4\\,\\,\\,\\,+4}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{\\,\\,\\,\\,\\,\\,\\,+4\\,\\,\\,\\,\\,\\,\\,+4}\\\\\\underline{2p}\\,\\,\\,\\,\\,\\,=\\underline{30}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{2p}\\,\\,\\,\\,\\,=\\,\\underline{-22}\\\\2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,2\\,\\,\\,\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,p=15\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,p=\\,-11\\end{array}[\/latex]<\/p>\n<p>Check the solutions in the original equation.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,\\left| 2p-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| 2p-4 \\right|=26\\\\\\left| 2(15)-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\left| 2(-11)-4 \\right|=26\\\\\\,\\,\\,\\,\\,\\left| 30-4 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| -22-4 \\right|=26\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| 26 \\right|=26\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left| -26 \\right|=26\\end{array}[\/latex]<\/p>\n<p>Both solutions check!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the next video, we show more examples of solving a simple absolute value equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2:  Solving Absolute Value Equations\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/4g-o_-mAFpc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Now let us look at an example where you need to do an algebraic step or two before you can write your two equations. The goal here is to get the absolute value on one side of the equation by itself. Then we can proceed as we did in the previous example.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve for <i>w<\/i>. [latex]3\\left|4w\u20131\\right|\u20135=10[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q303228\">Show Solution<\/span><\/p>\n<div id=\"q303228\" class=\"hidden-answer\" style=\"display: none\">\n<p>Isolate the term with the absolute value by adding 5 to both sides.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}3\\left|4w-1\\right|-5=10\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+5\\,\\,\\,+5}\\\\ 3\\left|4w-1\\right|=15\\end{array}[\/latex]<\/p>\n<p>Divide both sides by 3. Now the absolute value is isolated.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r} \\underline{3\\left|4w-1\\right|}=\\underline{15}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\,\\,\\\\\\left|4w-1\\right|=\\,\\,5\\end{array}[\/latex]<\/p>\n<p>Write the two equations that will give an absolute value of 5 and solve them.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{r}4w-1=5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4w-1=-5\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,+1\\,\\,+1}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{\\,\\,\\,\\,\\,\\,\\,\\,\\,+1\\,\\,\\,\\,\\,+1}\\\\\\,\\,\\,\\,\\,\\underline{4w}=\\underline{6}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{4w}\\,\\,\\,\\,\\,\\,\\,=\\underline{-4}\\\\4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,4\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,w=\\Large\\frac{3}{2}\\normalsize \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,w=-1\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,w=\\Large\\frac{3}{2}\\normalsize \\,\\,\\,\\,\\,\\text{or}\\,\\,\\,\\,\\,-1\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Check the solutions in the original equation.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\\\\\\\3\\left| 4\\left(\\Large\\frac{3}{2}\\normalsize\\right)-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 4w-1\\, \\right|-5=10\\\\\\\\\\,\\,\\,\\,\\,\\,3\\left|\\Large\\frac{12}{2}\\normalsize -1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,3\\left| 4(-1)-1\\, \\right|-5=10\\\\\\\\\\,\\,\\,\\,\\,\\,\\,\\,3\\left| 6-1\\, \\right|-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| -4-1\\, \\right|-5=10\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left(5\\right)-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\left| -5 \\right|-5=10\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,15-5=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,15-5=10\\\\10=10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,10=10\\end{array}[\/latex]<\/p>\n<p>Both solutions check!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the two videos that follow, we show examples of how to solve an absolute value equation that requires you to isolate the absolute value first using mathematical operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex 4:  Solving Absolute Value Equations (Requires Isolating Abs. Value)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-HrOMkIiSfU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Ex 5:  Solving Absolute Value Equations (Requires Isolating Abs. Value)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2bEA7HoDfpk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-77\">\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>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\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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) for Lumen Learning. <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><\/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":395986,"menu_order":4,"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\/dm-opentext\",\"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. Value)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/-HrOMkIiSfU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-77","chapter","type-chapter","status-publish","hentry"],"part":91,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/77\/revisions"}],"predecessor-version":[{"id":1481,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/77\/revisions\/1481"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/91"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/77\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=77"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=77"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=77"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}