{"id":4418,"date":"2020-04-13T12:57:42","date_gmt":"2020-04-13T12:57:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4418"},"modified":"2021-02-06T00:04:54","modified_gmt":"2021-02-06T00:04:54","slug":"using-the-subtraction-and-addition-properties-for-single-step-equations","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-the-subtraction-and-addition-properties-for-single-step-equations\/","title":{"raw":"Using the Subtraction and Addition Properties for Single-Step Equations","rendered":"Using the Subtraction and Addition Properties for Single-Step Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Determine whether a number is a solution to an equation<\/li><li>Review the use of the subtraction and addition properties of equality to solve linear equations<\/li><li>Use the addition and subtraction properties of equality to solve linear equations with fractions or decimals<\/li><\/ul><\/div>We began our work solving equations in previous chapters, where we said that solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.\n\n<div class=\"textbox shaded\"><h3 class=\"title\">Solution of an Equation<\/h3>A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.\n\nIn the earlier sections, we listed the steps to determine if a value is a solution. We restate them here.\n\nDetermine whether a number is a solution to an equation.\n\n<ol id=\"eip-95\" class=\"stepwise\"><li>Substitute the number for the variable in the equation.<\/li><li>Simplify the expressions on both sides of the equation.<\/li><li>Determine whether the resulting equation is true.<ul id=\"fs-id1703984\"><li>If it is true, the number is a solution.<\/li><li>If it is not true, the number is not a solution.<\/li><\/ul><\/li><\/ol><\/div>In the following example, we will show how to determine whether a number is a solution to an equation that contains addition and subtraction. You can use this idea to check your work later when you are solving equations.\n\n<div class=\"textbox exercises\"><h3>EXAMPLE<\/h3>Determine whether [latex]y=\\Large\\frac{3}{4}[\/latex] is a solution for [latex]4y+3=8y[\/latex].\n\nSolution:\n\n<table id=\"eip-id1168466426761\" class=\"unnumbered unstyled\" summary=\"The top line says 4y plus 3 equals 8y. Beside this is \"><tbody><tr><td><\/td><td>[latex]4y+3=8y[\/latex]<\/td><\/tr><tr><td>Substitute [latex]\\color{red}{\\Large\\frac{3}{4}}[\/latex] for [latex]y[\/latex]<\/td><td>[latex]4(\\color{red}{\\Large\\frac{3}{4}}\\normalsize)+3\\stackrel{\\text{?}}{=}8(\\color{red}{\\Large\\frac{3}{4}})[\/latex]<\/td><\/tr><tr><td>Multiply.<\/td><td>[latex]3+3\\stackrel{\\text{?}}{=}6[\/latex]<\/td><\/tr><tr><td>Add.<\/td><td>[latex]6=6\\quad\\checkmark[\/latex]<\/td><\/tr><\/tbody><\/table>Since [latex]y=\\Large\\frac{3}{4}[\/latex] results in a true equation, [latex]\\Large\\frac{3}{4}[\/latex] is a solution to the equation [latex]4y+3=8y[\/latex].\n\n<\/div>Now it is your turn to determine whether a fraction is the solution to an equation.\n\n<div class=\"textbox key-takeaways\"><h3>TRY IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141717&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\n\n\n\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141719&amp;theme=oea&amp;iframe_resize_id=mom3[\/embed]\n\n\n\n<\/div>We introduced the Subtraction and Addition Properties of Equality in Solving Equations Using the Subtraction and Addition Properties of Equality. In that section, we modeled how these properties work and then applied them to solving equations with whole numbers. We used these properties again each time we introduced a new system of numbers. Let\u2019s review those properties here.\n\n<div class=\"textbox shaded\"><h3 id=\"fs-id1956928\"><strong>Subtraction Property of Equality<\/strong><\/h3>For all real numbers [latex]a,b[\/latex], and [latex]c[\/latex], if [latex]a=b[\/latex], then [latex]a-c=b-c[\/latex].\n\n<\/div>&nbsp;\n\n<div class=\"textbox shaded\"><h3 id=\"fs-id1166490863495\"><strong>Addition Property of Equality<\/strong><\/h3>For all real numbers [latex]a,b[\/latex], and [latex]c[\/latex], if [latex]a=b[\/latex], then [latex]a+c=b+c[\/latex].\n\n<\/div>When you add or subtract the same quantity from both sides of an equation, you still have equality.\n\nWe introduced the Subtraction Property of Equality earlier by modeling equations with envelopes and counters. The image below&nbsp;models the equation [latex]x+3=8[\/latex].\n\n<figure id=\"CNX_BMath_Figure_08_01_026\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222533\/CNX_BMath_Figure_08_01_026.png\" alt=\"An envelope and three yellow counters are shown on the left side. On the right side are eight yellow counters.\"><\/figure>The goal is to isolate the variable on one side of the equation. So we \"took away\" [latex]3[\/latex] from both sides of the equation and found the solution [latex]x=5[\/latex].\n\nSome people picture a balance scale, as in the image below, when they solve equations.\n\n<figure id=\"CNX_BMath_Figure_08_01_001\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222535\/CNX_BMath_Figure_08_01_001.png\" alt=\"Three balance scales are shown. The top scale has one red weight on each side and is balanced. Beside it is \"><\/figure>The quantities on both sides of the equal sign in an equation are equal, or balanced. Just as with the balance scale, whatever you do to one side of the equation you must also do to the other to keep it balanced.\n\nIn the following example we&nbsp;review how to use Subtraction and Addition Properties of Equality to solve equations. We need to isolate the variable on one side of the equation. You can check your solutions by substituting the value into the equation to make sure you have a true statement.\n\n<div class=\"textbox exercises\"><h3>EXAMPLE<\/h3>Solve: [latex]x+11=-3[\/latex]\n[reveal-answer q=\"190834\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"190834\"]\n\nSolution:\nTo isolate [latex]x[\/latex], we undo the addition of [latex]11[\/latex] by using the Subtraction Property of Equality.\n\n<table id=\"eip-id1168468291100\" class=\"unnumbered unstyled\" summary=\"The top line says x plus 11 equals negative 3. The next line says, \"><tbody><tr><td colspan=\"2\"><\/td><td>[latex]x+11=-3[\/latex]<\/td><\/tr><tr><td colspan=\"2\">Subtract 11 from each side to \"undo\" the addition.<\/td><td>[latex]x+11\\color{red}{-11}=-3\\color{red}{-11}[\/latex]<\/td><\/tr><tr><td colspan=\"2\">Simplify.<\/td><td>[latex]x=-14[\/latex]<\/td><\/tr><tr><td>Check:<\/td><td>[latex]x+11=-3[\/latex]<\/td><td><\/td><\/tr><tr><td>Substitute [latex]x=-14[\/latex] .<\/td><td>[latex]\\color{red}{-14}+11\\stackrel{\\text{?}}{=}-3[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td>[latex]-3=-3\\quad\\checkmark[\/latex]<\/td><td><\/td><\/tr><\/tbody><\/table>Since [latex]x=-14[\/latex] makes [latex]x+11=-3[\/latex] a true statement, we know that it is a solution to the equation.\n\n[\/hidden-answer]\n\n<\/div>Now you can try solving an equation that requires using the addition property.\n\n<div class=\"textbox key-takeaways\"><h3>TRY IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141721&amp;theme=oea&amp;iframe_resize_id=mom200[\/embed]\n\n\n\n<\/div>In the original equation in the previous example, [latex]11[\/latex] was added to the [latex]x[\/latex] , so we subtracted [latex]11[\/latex] to \"undo\" the addition. In the next example, we will need to \"undo\" subtraction by using the Addition Property of Equality.\n\n<div class=\"textbox exercises\"><h3>EXAMPLE<\/h3>Solve: [latex]m - 4=-5[\/latex]\n[reveal-answer q=\"604060\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"604060\"]\n\nSolution:\n\n<table id=\"eip-id1168467157298\" class=\"unnumbered unstyled\" summary=\"The first line says m minus 4 equals negative 5. The next line says, \"><tbody><tr><td colspan=\"2\"><\/td><td>[latex]m-4=-5[\/latex]<\/td><\/tr><tr><td colspan=\"2\">Add 4 to each side to \"undo\" the subtraction.<\/td><td>[latex]m-4\\color{red}{+4}=-5\\color{red}{+4}[\/latex]<\/td><\/tr><tr><td colspan=\"2\">Simplify.<\/td><td>[latex]m=-1[\/latex]<\/td><\/tr><tr><td>Check:<\/td><td>[latex]m-4=-5[\/latex]<\/td><td><\/td><\/tr><tr><td>Substitute [latex]m=-1[\/latex] .<\/td><td>[latex]\\color{red}{-1}+4\\stackrel{\\text{?}}{=}-5[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td>[latex]-5=-5\\quad\\checkmark[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td><\/td><td>The solution to [latex]m - 4=-5[\/latex] is [latex]m=-1[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try using the addition property to solve an equation.\n\n<div class=\"textbox key-takeaways\"><h3>TRY&nbsp;IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141723&amp;theme=oea&amp;iframe_resize_id=mom27[\/embed]\n\n\n\n<\/div>In the following video, we present more examples of solving equations using the addition and subtraction properties.\n\nhttps:\/\/youtu.be\/yqdlj0lv7Cc\n\nYou may encounter equations that contain fractions, therefore in the following examples we will demonstrate how to use the addition property of equality to solve an equation with fractions.\n\n<div class=\"textbox exercises\"><h3>EXAMPLE<\/h3>Solve: [latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]\n[reveal-answer q=\"248157\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"248157\"]\n\nSolution:\n\n<table id=\"eip-id1168468255179\" class=\"unnumbered unstyled\" style=\"width: 602px\" summary=\"The first line says n minus 3 eighths equals one half. The next line says, \"><tbody><tr><td style=\"width: 313.391px\" colspan=\"2\"><\/td><td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/td><\/tr><tr><td style=\"width: 313.391px\" colspan=\"2\">Use the Addition Property of Equality.<\/td><td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize\\color{red}{+\\Large\\frac{3}{8}}\\normalsize =\\Large\\frac{1}{2}\\normalsize\\color{red}{+\\Large\\frac{3}{8}}[\/latex]<\/td><\/tr><tr><td style=\"width: 313.391px\" colspan=\"2\">Find the LCD to add the fractions on the right.<\/td><td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize +\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{4}{8}\\normalsize +\\Large\\frac{3}{8}[\/latex]<\/td><\/tr><tr><td style=\"width: 313.391px\" colspan=\"2\">Simplify.<\/td><td style=\"width: 255.609px\">[latex]n=\\Large\\frac{7}{8}[\/latex]<\/td><\/tr><tr><td style=\"width: 142px\">Check:<\/td><td style=\"width: 171.391px\">[latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/td><td style=\"width: 255.609px\"><\/td><\/tr><tr><td style=\"width: 142px\">Substitute [latex]n=\\color{red}{\\Large\\frac{7}{8}}[\/latex]<\/td><td style=\"width: 171.391px\">[latex]\\color{red}{\\Large\\frac{7}{8}}\\normalsize -\\Large\\frac{3}{8}\\normalsize\\stackrel{\\text{?}}{=}\\Large\\frac{1}{2}[\/latex]<\/td><td style=\"width: 255.609px\"><\/td><\/tr><tr><td style=\"width: 142px\">Subtract.<\/td><td style=\"width: 171.391px\">[latex]\\Large\\frac{4}{8}\\normalsize\\stackrel{\\text{?}}{=}\\Large\\frac{1}{2}[\/latex]<\/td><td style=\"width: 255.609px\"><\/td><\/tr><tr><td style=\"width: 142px\">Simplify.<\/td><td style=\"width: 171.391px\">[latex]\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{1}{2}\\normalsize\\quad\\checkmark[\/latex]<\/td><td style=\"width: 255.609px\"><\/td><\/tr><tr><td style=\"width: 142px\">The solution checks.<\/td><td style=\"width: 171.391px\"><\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try solving an equation with fractions by using the addition property of equality.\n\n<div class=\"textbox key-takeaways\"><h3>TRY&nbsp;IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141732&amp;theme=oea&amp;iframe_resize_id=mom25[\/embed]\n\n\n\n<\/div>Watch this video for more examples of solving equations that include fractions and require addition or subtraction.\n\nhttps:\/\/youtu.be\/KmOvCakGEgM\n\nYou may encounter equations with decimals, for example in financial or science applications. In the next examples we will demonstrate how to use the subtraction property of equality to solve equations with decimals.\n\n<div class=\"textbox exercises\"><h3>eXAMPLE<\/h3>Solve [latex]a - 3.7=4.3[\/latex]\n[reveal-answer q=\"652184\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"652184\"]\n\nSolution:\n\n<table id=\"eip-id1168468751492\" class=\"unnumbered unstyled\" style=\"width: 730px\" summary=\"The top line says a minus 3.7 equals 4.3. The next line says \"><tbody><tr><td style=\"width: 516.391px\" colspan=\"2\"><\/td><td style=\"width: 180.609px\">[latex]a-3.7=4.3[\/latex]<\/td><\/tr><tr><td style=\"width: 516.391px\" colspan=\"2\">Use the Addition Property of Equality.<\/td><td style=\"width: 180.609px\">[latex]a-3.7\\color{red}{+3.7}=4.3\\color{red}{+3.7}[\/latex]<\/td><\/tr><tr><td style=\"width: 516.391px\" colspan=\"2\">Add.<\/td><td style=\"width: 180.609px\">[latex]a=8[\/latex]<\/td><\/tr><tr><td style=\"width: 176px\">Check:<\/td><td style=\"width: 340.391px\">[latex]a-3.7=4.3[\/latex]<\/td><td style=\"width: 180.609px\"><\/td><\/tr><tr><td style=\"width: 176px\">Substitute [latex]a=8[\/latex] .<\/td><td style=\"width: 340.391px\">[latex]\\color{red}{8}-3.7\\stackrel{\\text{?}}{=}4.3[\/latex]<\/td><td style=\"width: 180.609px\"><\/td><\/tr><tr><td style=\"width: 176px\">Simplify.<\/td><td style=\"width: 340.391px\">[latex]4.3=4.3\\quad\\checkmark[\/latex]<\/td><td style=\"width: 180.609px\"><\/td><\/tr><tr><td style=\"width: 176px\">The solution checks.<\/td><td style=\"width: 340.391px\"><\/td><td style=\"width: 180.609px\"><\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now it is your turn to try solving an equation with decimals by using the addition property of equality.\n\n<div class=\"textbox key-takeaways\"><h3>TRY&nbsp;IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141736&amp;theme=oea&amp;iframe_resize_id=mom29[\/embed]\n\n\n\n<\/div>In this video, we show more examples of how to solve equations with decimals that require addition and subtraction.\n\nhttps:\/\/youtu.be\/a6YYJN_bHKs\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine whether a number is a solution to an equation<\/li>\n<li>Review the use of the subtraction and addition properties of equality to solve linear equations<\/li>\n<li>Use the addition and subtraction properties of equality to solve linear equations with fractions or decimals<\/li>\n<\/ul>\n<\/div>\n<p>We began our work solving equations in previous chapters, where we said that solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Solution of an Equation<\/h3>\n<p>A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/p>\n<p>In the earlier sections, we listed the steps to determine if a value is a solution. We restate them here.<\/p>\n<p>Determine whether a number is a solution to an equation.<\/p>\n<ol id=\"eip-95\" class=\"stepwise\">\n<li>Substitute the number for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting equation is true.\n<ul id=\"fs-id1703984\">\n<li>If it is true, the number is a solution.<\/li>\n<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<p>In the following example, we will show how to determine whether a number is a solution to an equation that contains addition and subtraction. You can use this idea to check your work later when you are solving equations.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Determine whether [latex]y=\\Large\\frac{3}{4}[\/latex] is a solution for [latex]4y+3=8y[\/latex].<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168466426761\" class=\"unnumbered unstyled\" summary=\"The top line says 4y plus 3 equals 8y. Beside this is\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4y+3=8y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{\\Large\\frac{3}{4}}[\/latex] for [latex]y[\/latex]<\/td>\n<td>[latex]4(\\color{red}{\\Large\\frac{3}{4}}\\normalsize)+3\\stackrel{\\text{?}}{=}8(\\color{red}{\\Large\\frac{3}{4}})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]3+3\\stackrel{\\text{?}}{=}6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]6=6\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since [latex]y=\\Large\\frac{3}{4}[\/latex] results in a true equation, [latex]\\Large\\frac{3}{4}[\/latex] is a solution to the equation [latex]4y+3=8y[\/latex].<\/p>\n<\/div>\n<p>Now it is your turn to determine whether a fraction is the solution to an equation.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141717\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141717&#38;theme=oea&#38;iframe_resize_id=ohm141717&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm141719\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141719&#38;theme=oea&#38;iframe_resize_id=ohm141719&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>We introduced the Subtraction and Addition Properties of Equality in Solving Equations Using the Subtraction and Addition Properties of Equality. In that section, we modeled how these properties work and then applied them to solving equations with whole numbers. We used these properties again each time we introduced a new system of numbers. Let\u2019s review those properties here.<\/p>\n<div class=\"textbox shaded\">\n<h3 id=\"fs-id1956928\"><strong>Subtraction Property of Equality<\/strong><\/h3>\n<p>For all real numbers [latex]a,b[\/latex], and [latex]c[\/latex], if [latex]a=b[\/latex], then [latex]a-c=b-c[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3 id=\"fs-id1166490863495\"><strong>Addition Property of Equality<\/strong><\/h3>\n<p>For all real numbers [latex]a,b[\/latex], and [latex]c[\/latex], if [latex]a=b[\/latex], then [latex]a+c=b+c[\/latex].<\/p>\n<\/div>\n<p>When you add or subtract the same quantity from both sides of an equation, you still have equality.<\/p>\n<p>We introduced the Subtraction Property of Equality earlier by modeling equations with envelopes and counters. The image below&nbsp;models the equation [latex]x+3=8[\/latex].<\/p>\n<figure id=\"CNX_BMath_Figure_08_01_026\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222533\/CNX_BMath_Figure_08_01_026.png\" alt=\"An envelope and three yellow counters are shown on the left side. On the right side are eight yellow counters.\" \/><\/figure>\n<p>The goal is to isolate the variable on one side of the equation. So we &#8220;took away&#8221; [latex]3[\/latex] from both sides of the equation and found the solution [latex]x=5[\/latex].<\/p>\n<p>Some people picture a balance scale, as in the image below, when they solve equations.<\/p>\n<figure id=\"CNX_BMath_Figure_08_01_001\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222535\/CNX_BMath_Figure_08_01_001.png\" alt=\"Three balance scales are shown. The top scale has one red weight on each side and is balanced. Beside it is\" \/><\/figure>\n<p>The quantities on both sides of the equal sign in an equation are equal, or balanced. Just as with the balance scale, whatever you do to one side of the equation you must also do to the other to keep it balanced.<\/p>\n<p>In the following example we&nbsp;review how to use Subtraction and Addition Properties of Equality to solve equations. We need to isolate the variable on one side of the equation. You can check your solutions by substituting the value into the equation to make sure you have a true statement.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Solve: [latex]x+11=-3[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190834\">Show Solution<\/span><\/p>\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nTo isolate [latex]x[\/latex], we undo the addition of [latex]11[\/latex] by using the Subtraction Property of Equality.<\/p>\n<table id=\"eip-id1168468291100\" class=\"unnumbered unstyled\" summary=\"The top line says x plus 11 equals negative 3. The next line says,\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]x+11=-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Subtract 11 from each side to &#8220;undo&#8221; the addition.<\/td>\n<td>[latex]x+11\\color{red}{-11}=-3\\color{red}{-11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]x=-14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]x+11=-3[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]x=-14[\/latex] .<\/td>\n<td>[latex]\\color{red}{-14}+11\\stackrel{\\text{?}}{=}-3[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-3=-3\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since [latex]x=-14[\/latex] makes [latex]x+11=-3[\/latex] a true statement, we know that it is a solution to the equation.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try solving an equation that requires using the addition property.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141721\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141721&#38;theme=oea&#38;iframe_resize_id=ohm141721&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the original equation in the previous example, [latex]11[\/latex] was added to the [latex]x[\/latex] , so we subtracted [latex]11[\/latex] to &#8220;undo&#8221; the addition. In the next example, we will need to &#8220;undo&#8221; subtraction by using the Addition Property of Equality.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Solve: [latex]m - 4=-5[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q604060\">Show Solution<\/span><\/p>\n<div id=\"q604060\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467157298\" class=\"unnumbered unstyled\" summary=\"The first line says m minus 4 equals negative 5. The next line says,\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]m-4=-5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add 4 to each side to &#8220;undo&#8221; the subtraction.<\/td>\n<td>[latex]m-4\\color{red}{+4}=-5\\color{red}{+4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]m=-1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]m-4=-5[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]m=-1[\/latex] .<\/td>\n<td>[latex]\\color{red}{-1}+4\\stackrel{\\text{?}}{=}-5[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-5=-5\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>The solution to [latex]m - 4=-5[\/latex] is [latex]m=-1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try using the addition property to solve an equation.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY&nbsp;IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141723\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141723&#38;theme=oea&#38;iframe_resize_id=ohm141723&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video, we present more examples of solving equations using the addition and subtraction properties.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Solve One Step Equations By Add and Subtract Whole Numbers (Variable on Left)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/yqdlj0lv7Cc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You may encounter equations that contain fractions, therefore in the following examples we will demonstrate how to use the addition property of equality to solve an equation with fractions.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Solve: [latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q248157\">Show Solution<\/span><\/p>\n<div id=\"q248157\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468255179\" class=\"unnumbered unstyled\" style=\"width: 602px\" summary=\"The first line says n minus 3 eighths equals one half. The next line says,\">\n<tbody>\n<tr>\n<td style=\"width: 313.391px\" colspan=\"2\"><\/td>\n<td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 313.391px\" colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize\\color{red}{+\\Large\\frac{3}{8}}\\normalsize =\\Large\\frac{1}{2}\\normalsize\\color{red}{+\\Large\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 313.391px\" colspan=\"2\">Find the LCD to add the fractions on the right.<\/td>\n<td style=\"width: 255.609px\">[latex]n-\\Large\\frac{3}{8}\\normalsize +\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{4}{8}\\normalsize +\\Large\\frac{3}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 313.391px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 255.609px\">[latex]n=\\Large\\frac{7}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 142px\">Check:<\/td>\n<td style=\"width: 171.391px\">[latex]n-\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{1}{2}[\/latex]<\/td>\n<td style=\"width: 255.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 142px\">Substitute [latex]n=\\color{red}{\\Large\\frac{7}{8}}[\/latex]<\/td>\n<td style=\"width: 171.391px\">[latex]\\color{red}{\\Large\\frac{7}{8}}\\normalsize -\\Large\\frac{3}{8}\\normalsize\\stackrel{\\text{?}}{=}\\Large\\frac{1}{2}[\/latex]<\/td>\n<td style=\"width: 255.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 142px\">Subtract.<\/td>\n<td style=\"width: 171.391px\">[latex]\\Large\\frac{4}{8}\\normalsize\\stackrel{\\text{?}}{=}\\Large\\frac{1}{2}[\/latex]<\/td>\n<td style=\"width: 255.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 142px\">Simplify.<\/td>\n<td style=\"width: 171.391px\">[latex]\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{1}{2}\\normalsize\\quad\\checkmark[\/latex]<\/td>\n<td style=\"width: 255.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 142px\">The solution checks.<\/td>\n<td style=\"width: 171.391px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try solving an equation with fractions by using the addition property of equality.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY&nbsp;IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141732\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141732&#38;theme=oea&#38;iframe_resize_id=ohm141732&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video for more examples of solving equations that include fractions and require addition or subtraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Solve One Step Equations With Fraction by Adding or Subtracting\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/KmOvCakGEgM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You may encounter equations with decimals, for example in financial or science applications. In the next examples we will demonstrate how to use the subtraction property of equality to solve equations with decimals.<\/p>\n<div class=\"textbox exercises\">\n<h3>eXAMPLE<\/h3>\n<p>Solve [latex]a - 3.7=4.3[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q652184\">Show Solution<\/span><\/p>\n<div id=\"q652184\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468751492\" class=\"unnumbered unstyled\" style=\"width: 730px\" summary=\"The top line says a minus 3.7 equals 4.3. The next line says\">\n<tbody>\n<tr>\n<td style=\"width: 516.391px\" colspan=\"2\"><\/td>\n<td style=\"width: 180.609px\">[latex]a-3.7=4.3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 516.391px\" colspan=\"2\">Use the Addition Property of Equality.<\/td>\n<td style=\"width: 180.609px\">[latex]a-3.7\\color{red}{+3.7}=4.3\\color{red}{+3.7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 516.391px\" colspan=\"2\">Add.<\/td>\n<td style=\"width: 180.609px\">[latex]a=8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 176px\">Check:<\/td>\n<td style=\"width: 340.391px\">[latex]a-3.7=4.3[\/latex]<\/td>\n<td style=\"width: 180.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 176px\">Substitute [latex]a=8[\/latex] .<\/td>\n<td style=\"width: 340.391px\">[latex]\\color{red}{8}-3.7\\stackrel{\\text{?}}{=}4.3[\/latex]<\/td>\n<td style=\"width: 180.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 176px\">Simplify.<\/td>\n<td style=\"width: 340.391px\">[latex]4.3=4.3\\quad\\checkmark[\/latex]<\/td>\n<td style=\"width: 180.609px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 176px\">The solution checks.<\/td>\n<td style=\"width: 340.391px\"><\/td>\n<td style=\"width: 180.609px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now it is your turn to try solving an equation with decimals by using the addition property of equality.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY&nbsp;IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141736\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141736&#38;theme=oea&#38;iframe_resize_id=ohm141736&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In this video, we show more examples of how to solve equations with decimals that require addition and subtraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex:  Solve a One Step Equation With Decimals by Adding and Subtracting\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/a6YYJN_bHKs?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-4418\">\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>Question ID 141717, 141719, 141721, 141736, 141732. <strong>Authored 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>. <strong>License Terms<\/strong>: IMathAS Community License, CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Solve One Step Equations By Add and Subtract Whole Numbers (Variable on Left). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/yqdlj0lv7Cc\">https:\/\/youtu.be\/yqdlj0lv7Cc<\/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: Solve One Step Equations With Fraction by Adding or Subtracting. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/KmOvCakGEgM\">https:\/\/youtu.be\/KmOvCakGEgM<\/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: Solve a One Step Equation With Decimals by Adding and Subtracting. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/a6YYJN_bHKs\">https:\/\/youtu.be\/a6YYJN_bHKs<\/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, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":25777,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Solve One Step 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Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License, CC-BY + GPL\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4418","chapter","type-chapter","status-web-only","hentry"],"part":4412,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4418\/revisions"}],"predecessor-version":[{"id":4419,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4418\/revisions\/4419"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4412"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4418\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4418"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4418"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4418"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}