{"id":4527,"date":"2017-06-07T18:50:29","date_gmt":"2017-06-07T18:50:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-addition-property-of-equality\/"},"modified":"2017-08-15T12:17:28","modified_gmt":"2017-08-15T12:17:28","slug":"read-addition-property-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-addition-property-of-equality\/","title":{"raw":"Addition Property of Equality","rendered":"Addition Property of Equality"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Use the addition property of equality\r\n<ul>\r\n \t<li>Solve algebraic equations using the addition property of equality<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 id=\"title1\">Solve an algebraic equation using the addition property of equality<\/h2>\r\nFirst, let's define some important terminology:\r\n<ul>\r\n \t<li><strong>variables:\u00a0<\/strong> variables are symbols that stand for an unknown quantity, they are often represented with letters, like <i>x<\/i>, <i>y<\/i>, or <i>z<\/i>.<\/li>\r\n \t<li><strong>coefficient:\u00a0<\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of 3<i>x <\/i>is 3.<\/li>\r\n \t<li><strong>term:\u00a0<\/strong>a single number, or variables and numbers connected by multiplication. -4, 6x and [latex]x^2[\/latex] are all terms<\/li>\r\n \t<li><strong>expression: <\/strong>groups of terms connected by addition and subtraction.\u00a0 [latex]2x^2-5[\/latex] is an expression<\/li>\r\n \t<li><strong>equation: <\/strong>\u00a0an equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.\u00a0Think of an equal sign as meaning \"the same as.\" Some examples of equations are\u00a0[latex]y = mx +b[\/latex], \u00a0[latex]\\frac{3}{4}r = v^{3} - r[\/latex], and \u00a0[latex]2(6-d) + f(3 +k) = \\frac{1}{4}d[\/latex]<\/li>\r\n<\/ul>\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[caption id=\"attachment_4693\" align=\"aligncenter\" width=\"424\"]<img class=\"wp-image-4693\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185028\/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\" \/> Equation made of coefficients, variables, terms and expressions.[\/caption]\r\n<h3>Using the Addition Property of Equality<\/h3>\r\nAn important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. Sometimes people refer to this as keeping the equation \u201cbalanced.\u201d If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.\r\n\r\nLet\u2019s look at a simple numeric equation, [latex]3+7=10[\/latex], to explore the idea of an equation as being balanced.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/textimgs.s3.amazonaws.com\/MITEdevmath\/NROCUnit10_files\/image001.jpg#fixme#fixme\" alt=\"A balanced scale, with a 3 and a 7 one side and a 10 on the other.\" width=\"318\" height=\"217\" \/>\r\n\r\nThe expressions on each side of the equal sign are equal, so you can add the same value to each side and maintain the equality. Let\u2019s see what happens when 5 is added to each side.\r\n<p style=\"text-align: center\">[latex]3+7+5=10+5[\/latex]<\/p>\r\nSince each expression is equal to 15, you can see that adding 5 to each side of the original equation resulted in a true equation. The equation is still \u201cbalanced.\u201d\r\n\r\nOn the other hand, let\u2019s look at what would happen if you added 5 to only one side of the equation.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3+7=10\\\\3+7+5=10\\\\15\\neq 10\\end{array}[\/latex]<\/p>\r\nAdding 5 to only one side of the equation resulted in an equation that is false. The equation is no longer \u201cbalanced,\u201d and it is no longer a true equation!\r\n<div class=\"textbox shaded\">\r\n<h3>Addition Property of Equality<\/h3>\r\nFor all real numbers <i>a<\/i>, <i>b<\/i>, and <i>c<\/i>: If [latex]a=b[\/latex], then [latex]a+c=b+c[\/latex].\r\n\r\nIf two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.\r\n\r\n<\/div>\r\n<h3>Solve algebraic equations using the addition property of equality<\/h3>\r\nWhen you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you <b>isolate the variable<\/b>. Isolating the variable means rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation.\r\n\r\nWhen the equation involves addition or subtraction, use the inverse operation to \u201cundo\u201d the operation in order to isolate the variable. For addition and subtraction, your goal is to change any value being added or subtracted to 0, the additive identity.\r\n\r\nIn the following simulation, you can adjust the quantity being added or subtracted to each side of an equation to see how important it is to perform the same operation on both sides of an equation when you are solving.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Examples<\/h3>\r\nSolve [latex]x-6=8[\/latex].\r\n\r\n[reveal-answer q=\"577240\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"577240\"]\r\n\r\nThis equation means that if you begin with some unknown number, <i>x<\/i>, and subtract 6, you will end up with 8. You are trying to figure out the value of the variable <i>x.<\/i>\r\n\r\nUsing the Addition Property of Equality, add 6 to both sides of the equation to isolate the variable. You choose to add 6 because 6 is being subtracted from the variable.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}x-6\\,\\,\\,=\\,\\,\\,\\,8\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{+\\,6\\,\\,\\,\\,\\,\\,\\,\\,+6}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,=\\, 14\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=14[\/latex]\r\n\r\n[\/hidden-answer]\r\nSolve [latex]x+5=27[\/latex].\r\n\r\n[reveal-answer q=\"579240\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"579240\"]\r\n\r\nThis equation means that if you begin with some unknown number, <i>x<\/i>, and add 5, you will end up with 27. You are trying to figure out the value of the variable <i>x.<\/i>\r\n\r\nUsing the Addition Property of Equality, subtract 5 from both sides of the equation to isolate the variable. You choose to subtract 5, as 5 is being added from the variable.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}x+5\\,\\,=\\,\\,27\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-5\\,\\,\\,\\,\\,\\,\\,\\,-5}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,=\\, 22\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=22[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video two examples of using the addition property of equality are shown.\r\nhttps:\/\/youtu.be\/VsWrFKFerSY\r\nSince subtraction can be written as addition (adding the opposite), the <b>addition property of equality<\/b> can be used for subtraction as well. So just as you can add the same value to each side of an equation without changing the meaning of the equation, you can subtract the same value from each side of an equation.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Examples<\/h3>\r\nSolve [latex]x+10=-65[\/latex]. Check your solution.\r\n\r\n[reveal-answer q=\"684455\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"684455\"]\r\n\r\nSolve:\r\n<p style=\"text-align: center\">[latex]x+10=-65[\/latex]<\/p>\r\nSince 10 is being added to the variable, subtract 10 from both sides. Note that subtracting 10 is the same as adding [latex]\u201310[\/latex].\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}x+10\\,\\,=\\,\\,\\,\\,-65\\\\\\,\\,\\,\\,\\,\\underline{-10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-10}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,\\,=\\,\\,\\,-75\\end{array}[\/latex]<\/p>\r\nTo check, substitute the solution, [latex]\u201375[\/latex] for <i>x <\/i>in the original equation, then simplify.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,x+10\\,\\,\\,=-65\\\\-75+\\,10\\,\\,\\,=-65\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-65\\,\\,\\,=-65\\end{array}[\/latex]<\/p>\r\nThis equation is true, so the solution is correct.\r\n<h4>Answer<\/h4>\r\n[latex]x=\u201375[\/latex] is the solution to the equation [latex]x+10=\u201365[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\nSolve [latex]x-4=-32[\/latex]. Check your solution.\r\n\r\n[reveal-answer q=\"624455\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"624455\"]\r\n\r\nSolve:\r\n<p style=\"text-align: center\">[latex]x-4=-32[\/latex]<\/p>\r\nSince 4 is being subtracted from\u00a0the variable, add 4 to\u00a0both sides.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}x-4\\,\\,=\\,\\,\\,\\,-32\\\\\\,\\,\\,\\,\\,\\underline{+4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+4}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,\\,=\\,\\,\\,-28\\end{array}[\/latex]<\/p>\r\nCheck:\r\n\r\nTo check, substitute the solution, [latex]\u201328[\/latex] for <i>x <\/i>in the original equation, then simplify.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,x-4\\,\\,\\,=-32\\\\-28-\\,4\\,\\,\\,=-32\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-32\\,\\,\\,=-32\\end{array}[\/latex]<\/p>\r\nThis equation is true, so the solution is correct.\r\n<h4>Answer<\/h4>\r\n[latex]x=\u201328[\/latex] is the solution to the equation [latex]x-4=\u201332[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIt is always a good idea to check your answer whether you are\u00a0requested to or not.\r\n\r\nThe following video presents two examples of using the addition property of equality when there are negative integers in the equation.\r\n\r\nhttps:\/\/youtu.be\/D3T8eCT5U_w\r\n<div class=\"bcc-box bcc-success\">\r\n<h3>Think About It<\/h3>\r\nCan you determine\u00a0what you would do differently if you were asked to solve equations like these?\r\n\r\na) Solve [latex]{12.5}+{ t }= {-7.5}[\/latex].\r\n\r\nWhat makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would solve this equation with decimals.\r\n\r\n[practice-area rows=\"2\"][\/practice-area]\r\n\r\n[reveal-answer q=\"680980\"]Show Solution[\/reveal-answer]\r\n\r\n[hidden-answer a=\"680980\"]To solve this equation you need to remember how to\u00a0add or subtract decimal numbers. You also need to remember that when you subtract a number from a negative number, your result will be negative.\r\n\r\nUsing the Addition Property of Equality, subtract 12.5 from both sides of the equation to isolate the variable, <em>t<\/em>. You choose to\u00a0subtract\u00a012.5 because\u00a012.5 is being added to the variable, <em>t<\/em>.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}{12.5}+{t}\\,\\,\\,=\\,\\,\\,\\,{-7.5}\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-12.5\\,\\,\\,\\,\\,\\,\\,\\,-12.5}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,t\\,\\,=\\, -20\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">To add two numbers of the same sign,\u00a0first add their absolute values:<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\left|-12.5\\right| = 12.5\\\\\\left|-7.5\\right| = 7.5\\,\\,\\,\\\\12.5 + 7.5 = 20\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">Now apply the sign they share, which is negative:<\/p>\r\n<p style=\"text-align: center\">[latex]-12.5 -7.5 = -20[\/latex]<\/p>\r\n<p style=\"text-align: center\">[\/hidden-answer]<\/p>\r\nb) Solve [latex]\\frac{1}{4} + y = 3[\/latex]. What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would solve this equation with a fraction.\r\n\r\n[practice-area rows=\"2\"][\/practice-area]\r\n\r\n[reveal-answer q=\"690980\"]Show Solution[\/reveal-answer]\r\n\r\n[hidden-answer a=\"690980\"]\r\n\r\nUsing the Addition Property of Equality, subtract [latex]\\frac{1}{4}[\/latex] from both sides of the equation to isolate the variable, <em>y<\/em>. You choose to\u00a0subtract [latex]\\frac{1}{4}[\/latex] as [latex]\\frac{1}{4}[\/latex] is being added to the variable, <em>y<\/em>.\r\n<p style=\"text-align: center\">[latex]\\displaystyle\\begin{array}{r}\\frac{1}{4} + y\\,\\,\\,=\\,\\,\\,\\,{3}\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-\\frac{1}{4}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-\\frac{1}{4}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,=\\,3-\\frac{1}{4}\\,\\,\\end{array}[\/latex]<\/p>\r\nTo subtract\u00a0[latex]\\frac{1}{4}[\/latex] from 3, you need a common denominator.\r\n\r\nMake 3 into a fraction by dividing by 1,\u00a0[latex]\\frac{3}{1}[\/latex]. \u00a0Your denominators are 1 and 4. The least common multiple is 4.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{3}{1}\\cdot\\frac{4}{4}=\\frac{12}{4}\\\\\\frac{12}{4} -\\frac{1}{4} =\\frac{11}{4}\\end{array}[\/latex]<\/p>\r\nTherefore, [latex]y =3 -\\frac{1}{4} =\\frac{11}{4}[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, two examples of using the addition property of equality with decimal numbers are shown.\r\n\r\nhttps:\/\/youtu.be\/D8wKGlxf6bM\r\n\r\nThe next video shows how to use the addition property of equality to solve equations with fractions.\r\n\r\nhttps:\/\/youtu.be\/O7SPM7Cs8Ds\r\n\r\nThe examples above are sometimes called <b>one-step equations<\/b> because they require only one step to solve. In these examples, you either added or subtracted a <b>constant<\/b> from both sides of the equation to isolate the variable and solve the equation.\r\n\r\nWith any equation, you can check your solution by substituting the value for the variable in the original equation. In other words, you evaluate the original equation using your solution. If you get a true statement, then your solution is correct.\r\n\r\n&nbsp;","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Use the addition property of equality\n<ul>\n<li>Solve algebraic equations using the addition property of equality<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2 id=\"title1\">Solve an algebraic equation using the addition property of equality<\/h2>\n<p>First, let&#8217;s define some important terminology:<\/p>\n<ul>\n<li><strong>variables:\u00a0<\/strong> variables are symbols that stand for an unknown quantity, they are often represented with letters, like <i>x<\/i>, <i>y<\/i>, or <i>z<\/i>.<\/li>\n<li><strong>coefficient:\u00a0<\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of 3<i>x <\/i>is 3.<\/li>\n<li><strong>term:\u00a0<\/strong>a single number, or variables and numbers connected by multiplication. -4, 6x and [latex]x^2[\/latex] are all terms<\/li>\n<li><strong>expression: <\/strong>groups of terms connected by addition and subtraction.\u00a0 [latex]2x^2-5[\/latex] is an expression<\/li>\n<li><strong>equation: <\/strong>\u00a0an equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.\u00a0Think of an equal sign as meaning &#8220;the same as.&#8221; Some examples of equations are\u00a0[latex]y = mx +b[\/latex], \u00a0[latex]\\frac{3}{4}r = v^{3} - r[\/latex], and \u00a0[latex]2(6-d) + f(3 +k) = \\frac{1}{4}d[\/latex]<\/li>\n<\/ul>\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<div id=\"attachment_4693\" style=\"width: 434px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4693\" class=\"wp-image-4693\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185028\/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 id=\"caption-attachment-4693\" class=\"wp-caption-text\">Equation made of coefficients, variables, terms and expressions.<\/p>\n<\/div>\n<h3>Using the Addition Property of Equality<\/h3>\n<p>An important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. Sometimes people refer to this as keeping the equation \u201cbalanced.\u201d If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.<\/p>\n<p>Let\u2019s look at a simple numeric equation, [latex]3+7=10[\/latex], to explore the idea of an equation as being balanced.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/textimgs.s3.amazonaws.com\/MITEdevmath\/NROCUnit10_files\/image001.jpg#fixme#fixme\" alt=\"A balanced scale, with a 3 and a 7 one side and a 10 on the other.\" width=\"318\" height=\"217\" \/><\/p>\n<p>The expressions on each side of the equal sign are equal, so you can add the same value to each side and maintain the equality. Let\u2019s see what happens when 5 is added to each side.<\/p>\n<p style=\"text-align: center\">[latex]3+7+5=10+5[\/latex]<\/p>\n<p>Since each expression is equal to 15, you can see that adding 5 to each side of the original equation resulted in a true equation. The equation is still \u201cbalanced.\u201d<\/p>\n<p>On the other hand, let\u2019s look at what would happen if you added 5 to only one side of the equation.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3+7=10\\\\3+7+5=10\\\\15\\neq 10\\end{array}[\/latex]<\/p>\n<p>Adding 5 to only one side of the equation resulted in an equation that is false. The equation is no longer \u201cbalanced,\u201d and it is no longer a true equation!<\/p>\n<div class=\"textbox shaded\">\n<h3>Addition Property of Equality<\/h3>\n<p>For all real numbers <i>a<\/i>, <i>b<\/i>, and <i>c<\/i>: If [latex]a=b[\/latex], then [latex]a+c=b+c[\/latex].<\/p>\n<p>If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.<\/p>\n<\/div>\n<h3>Solve algebraic equations using the addition property of equality<\/h3>\n<p>When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you <b>isolate the variable<\/b>. Isolating the variable means rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation.<\/p>\n<p>When the equation involves addition or subtraction, use the inverse operation to \u201cundo\u201d the operation in order to isolate the variable. For addition and subtraction, your goal is to change any value being added or subtracted to 0, the additive identity.<\/p>\n<p>In the following simulation, you can adjust the quantity being added or subtracted to each side of an equation to see how important it is to perform the same operation on both sides of an equation when you are solving.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Examples<\/h3>\n<p>Solve [latex]x-6=8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q577240\">Show Solution<\/span><\/p>\n<div id=\"q577240\" class=\"hidden-answer\" style=\"display: none\">\n<p>This equation means that if you begin with some unknown number, <i>x<\/i>, and subtract 6, you will end up with 8. You are trying to figure out the value of the variable <i>x.<\/i><\/p>\n<p>Using the Addition Property of Equality, add 6 to both sides of the equation to isolate the variable. You choose to add 6 because 6 is being subtracted from the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}x-6\\,\\,\\,=\\,\\,\\,\\,8\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{+\\,6\\,\\,\\,\\,\\,\\,\\,\\,+6}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,=\\, 14\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=14[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>Solve [latex]x+5=27[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q579240\">Show Solution<\/span><\/p>\n<div id=\"q579240\" class=\"hidden-answer\" style=\"display: none\">\n<p>This equation means that if you begin with some unknown number, <i>x<\/i>, and add 5, you will end up with 27. You are trying to figure out the value of the variable <i>x.<\/i><\/p>\n<p>Using the Addition Property of Equality, subtract 5 from both sides of the equation to isolate the variable. You choose to subtract 5, as 5 is being added from the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}x+5\\,\\,=\\,\\,27\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-5\\,\\,\\,\\,\\,\\,\\,\\,-5}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,=\\, 22\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=22[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video two examples of using the addition property of equality are shown.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solve One-Step Equations Using Addition and Subtraction  (Whole Numbers)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/VsWrFKFerSY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\nSince subtraction can be written as addition (adding the opposite), the <b>addition property of equality<\/b> can be used for subtraction as well. So just as you can add the same value to each side of an equation without changing the meaning of the equation, you can subtract the same value from each side of an equation.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Examples<\/h3>\n<p>Solve [latex]x+10=-65[\/latex]. Check your solution.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q684455\">Show Solution<\/span><\/p>\n<div id=\"q684455\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solve:<\/p>\n<p style=\"text-align: center\">[latex]x+10=-65[\/latex]<\/p>\n<p>Since 10 is being added to the variable, subtract 10 from both sides. Note that subtracting 10 is the same as adding [latex]\u201310[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}x+10\\,\\,=\\,\\,\\,\\,-65\\\\\\,\\,\\,\\,\\,\\underline{-10\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-10}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,\\,=\\,\\,\\,-75\\end{array}[\/latex]<\/p>\n<p>To check, substitute the solution, [latex]\u201375[\/latex] for <i>x <\/i>in the original equation, then simplify.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,x+10\\,\\,\\,=-65\\\\-75+\\,10\\,\\,\\,=-65\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-65\\,\\,\\,=-65\\end{array}[\/latex]<\/p>\n<p>This equation is true, so the solution is correct.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=\u201375[\/latex] is the solution to the equation [latex]x+10=\u201365[\/latex].<\/p>\n<\/div>\n<\/div>\n<p>Solve [latex]x-4=-32[\/latex]. Check your solution.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q624455\">Show Solution<\/span><\/p>\n<div id=\"q624455\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solve:<\/p>\n<p style=\"text-align: center\">[latex]x-4=-32[\/latex]<\/p>\n<p>Since 4 is being subtracted from\u00a0the variable, add 4 to\u00a0both sides.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}x-4\\,\\,=\\,\\,\\,\\,-32\\\\\\,\\,\\,\\,\\,\\underline{+4\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+4}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,\\,=\\,\\,\\,-28\\end{array}[\/latex]<\/p>\n<p>Check:<\/p>\n<p>To check, substitute the solution, [latex]\u201328[\/latex] for <i>x <\/i>in the original equation, then simplify.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}\\,\\,\\,\\,\\,x-4\\,\\,\\,=-32\\\\-28-\\,4\\,\\,\\,=-32\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-32\\,\\,\\,=-32\\end{array}[\/latex]<\/p>\n<p>This equation is true, so the solution is correct.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=\u201328[\/latex] is the solution to the equation [latex]x-4=\u201332[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>It is always a good idea to check your answer whether you are\u00a0requested to or not.<\/p>\n<p>The following video presents two examples of using the addition property of equality when there are negative integers in the equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Solving One Step Equations Using Addition and Subtraction (Integers)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/D3T8eCT5U_w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"bcc-box bcc-success\">\n<h3>Think About It<\/h3>\n<p>Can you determine\u00a0what you would do differently if you were asked to solve equations like these?<\/p>\n<p>a) Solve [latex]{12.5}+{ t }= {-7.5}[\/latex].<\/p>\n<p>What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would solve this equation with decimals.<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"2\"><\/textarea><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q680980\">Show Solution<\/span><\/p>\n<div id=\"q680980\" class=\"hidden-answer\" style=\"display: none\">To solve this equation you need to remember how to\u00a0add or subtract decimal numbers. You also need to remember that when you subtract a number from a negative number, your result will be negative.<\/p>\n<p>Using the Addition Property of Equality, subtract 12.5 from both sides of the equation to isolate the variable, <em>t<\/em>. You choose to\u00a0subtract\u00a012.5 because\u00a012.5 is being added to the variable, <em>t<\/em>.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}{12.5}+{t}\\,\\,\\,=\\,\\,\\,\\,{-7.5}\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-12.5\\,\\,\\,\\,\\,\\,\\,\\,-12.5}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,t\\,\\,=\\, -20\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">To add two numbers of the same sign,\u00a0first add their absolute values:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\left|-12.5\\right| = 12.5\\\\\\left|-7.5\\right| = 7.5\\,\\,\\,\\\\12.5 + 7.5 = 20\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">Now apply the sign they share, which is negative:<\/p>\n<p style=\"text-align: center\">[latex]-12.5 -7.5 = -20[\/latex]<\/p>\n<p style=\"text-align: center\"><\/div>\n<\/div>\n<p>b) Solve [latex]\\frac{1}{4} + y = 3[\/latex]. What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would solve this equation with a fraction.<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"2\"><\/textarea><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q690980\">Show Solution<\/span><\/p>\n<div id=\"q690980\" class=\"hidden-answer\" style=\"display: none\">\n<p>Using the Addition Property of Equality, subtract [latex]\\frac{1}{4}[\/latex] from both sides of the equation to isolate the variable, <em>y<\/em>. You choose to\u00a0subtract [latex]\\frac{1}{4}[\/latex] as [latex]\\frac{1}{4}[\/latex] is being added to the variable, <em>y<\/em>.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle\\begin{array}{r}\\frac{1}{4} + y\\,\\,\\,=\\,\\,\\,\\,{3}\\,\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\underline{-\\frac{1}{4}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-\\frac{1}{4}}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,=\\,3-\\frac{1}{4}\\,\\,\\end{array}[\/latex]<\/p>\n<p>To subtract\u00a0[latex]\\frac{1}{4}[\/latex] from 3, you need a common denominator.<\/p>\n<p>Make 3 into a fraction by dividing by 1,\u00a0[latex]\\frac{3}{1}[\/latex]. \u00a0Your denominators are 1 and 4. The least common multiple is 4.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{3}{1}\\cdot\\frac{4}{4}=\\frac{12}{4}\\\\\\frac{12}{4} -\\frac{1}{4} =\\frac{11}{4}\\end{array}[\/latex]<\/p>\n<p>Therefore, [latex]y =3 -\\frac{1}{4} =\\frac{11}{4}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, two examples of using the addition property of equality with decimal numbers are shown.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Solving One Step Equations Using Addition and Subtraction (Decimals)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/D8wKGlxf6bM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The next video shows how to use the addition property of equality to solve equations with fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Solving One Step Equations Using Addition and Subtraction (Fractions)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/O7SPM7Cs8Ds?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The examples above are sometimes called <b>one-step equations<\/b> because they require only one step to solve. In these examples, you either added or subtracted a <b>constant<\/b> from both sides of the equation to isolate the variable and solve the equation.<\/p>\n<p>With any equation, you can check your solution by substituting the value for the variable in the original equation. In other words, you evaluate the original equation using your solution. If you get a true statement, then your solution is correct.<\/p>\n<p>&nbsp;<\/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-4527\">\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>Graphic: Equation, term, expression. <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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Solve One-Step Equations Using Addition and Subtraction (Whole Numbers). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/VsWrFKFerSY\">https:\/\/youtu.be\/VsWrFKFerSY<\/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 One Step Equations Using Addition and Subtraction (Integers). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/D3T8eCT5U_w\">https:\/\/youtu.be\/D3T8eCT5U_w<\/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 One Step Equations Using Addition and Subtraction (Decimals). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/D8wKGlxf6bM\">https:\/\/youtu.be\/D8wKGlxf6bM<\/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 One Step Equations Using Addition and Subtraction (Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/O7SPM7Cs8Ds\">https:\/\/youtu.be\/O7SPM7Cs8Ds<\/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 1: Solving Absolute Value Equations. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/U-7fF-W8_xE\">https:\/\/youtu.be\/U-7fF-W8_xE<\/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>Unit 10: Solving Equations and Inequalities, First Edition Developmental Math: An Open Program . <strong>Provided by<\/strong>: Monterey Institute of Technology. <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><\/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":17533,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Solve One-Step Equations Using Addition and Subtraction (Whole 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