{"id":3564,"date":"2019-12-31T17:03:27","date_gmt":"2019-12-31T17:03:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3564"},"modified":"2025-09-02T18:19:08","modified_gmt":"2025-09-02T18:19:08","slug":"simplifying-expressions-with-absolute-value","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/simplifying-expressions-with-absolute-value\/","title":{"raw":"Simplifying Expressions With Absolute Value","rendered":"Simplifying Expressions With Absolute Value"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use correct notation to indicate absolute value<\/li>\r\n \t<li>Simplify expressions that contain\u00a0absolute value<\/li>\r\n \t<li>Evaluate expressions that contain absolute value<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe saw that numbers such as [latex]5[\/latex] and [latex]-5[\/latex] are opposites because they are the same distance from [latex]0[\/latex] on the number line. They are both five units from [latex]0[\/latex]. The distance between [latex]0[\/latex] and any number on the number line is called the absolute value of that number.\r\n\r\nBecause distance is never negative, the absolute value of any number is never negative.\r\n\r\nThe symbol for absolute value is two vertical lines on either side of a number. So the absolute value of [latex]5[\/latex] is written as [latex]|5|[\/latex], and the absolute value of [latex]-5[\/latex] is written as [latex]|-5|[\/latex] as shown below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220135\/CNX_BMath_Figure_03_01_019.png\" alt=\"This figure is a number line. The points negative 5 and 5 are labeled. Above the number line the distance from negative 5 to 0 is labeled as 5 units. Also above the number line the distance from 0 to 5 is labeled as 5 units.\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Absolute Value<\/h3>\r\nThe absolute value of a number is its distance from [latex]0[\/latex] on the number line.\r\nThe absolute value of a number [latex]n[\/latex] is written as [latex]|n|[\/latex].\r\n\r\n[latex]|n|\\ge 0[\/latex] for all numbers\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n<ol>\r\n \t<li>\u00a0[latex]|3|[\/latex]<\/li>\r\n \t<li>\u00a0[latex]|-44|[\/latex]<\/li>\r\n \t<li>\u00a0[latex]|0|[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n<table id=\"eip-id1165118025864\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|3|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex] is [latex]3[\/latex] units from zero.<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1171842979184\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|-44|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\u221244[\/latex] is [latex]44[\/latex] units from zero.<\/td>\r\n<td>[latex]44[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1171842583307\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|0|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex] is already at zero.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]144930[\/ohm_question]\r\n\r\n[ohm_question hide_question_numbers=1]144931[\/ohm_question]\r\n\r\n[ohm_question hide_question_numbers=1]144932[\/ohm_question]\r\n\r\n[ohm_question hide_question_numbers=1]144933[\/ohm_question]\r\n\r\n<\/div>\r\nIn the video below we show another example of how to find the absolute value of an integer.\r\n\r\nhttps:\/\/youtu.be\/I8bTqGmkqGI\r\n\r\nWe treat absolute value bars just like we treat parentheses in the order of operations. We simplify the expression inside first.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate:\r\n<ol>\r\n \t<li>[latex]|x|\\text{ when }x=-35[\/latex]<\/li>\r\n \t<li>[latex]|\\mathit{\\text{-y}}|\\text{ when }y=-20[\/latex]<\/li>\r\n \t<li>[latex]-|u|\\text{ when }u=12[\/latex]<\/li>\r\n \t<li>[latex]-|p|\\text{ when }p=-14[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"727778\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"727778\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466007339\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has the absolute value of x. The second row states to substitute negative 35 for x and has the absolute value symbol with negative 35. The third row states to take the absolute value and has 35.\">\r\n<tbody>\r\n<tr>\r\n<td>1. To find [latex]|x|[\/latex] when [latex]x=-35:[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|x|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{-35}[\/latex] for x.<\/td>\r\n<td>[latex]\\mid\\color{red}{-35}\\mid[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469585161\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has four rows. The first row has the absolute value of y. The second row states to substitute negative 20 for y and has inside of the absolute value symbol a negative sign with negative 20 inside of parentheses. The third row states to simplify and has 20 inside of the absolute value symbol. The fourth row states to take the absolute value and has 20.\">\r\n<tbody>\r\n<tr>\r\n<td>2. To find [latex]|-y|[\/latex] when [latex]y=-20:[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|-y|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{-20}[\/latex] for y.<\/td>\r\n<td>[latex]\\mid-(\\color{red}{-20})\\mid[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]|20|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]20[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466911241\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has a negative sign in front of the absolute value of u. The second row states to substitute 12 for u and has a negative sign in front of the absolute value symbol with 12 on the inside. The third row states to take the absolute value and has negative 12.\">\r\n<tbody>\r\n<tr>\r\n<td>3. To find [latex]-|u|[\/latex] when [latex]u=12:[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-|u|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{12}[\/latex] for u.<\/td>\r\n<td>[latex]-\\mid\\color{red}{12}\\mid[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]-12[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468381460\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has a negative sign in front of the absolute value of p. The second row states to substitute negative 14 for p and has a negative sign in front of the absolute value of negative 14. The third row states to take the absolute value and has negative 14.\">\r\n<tbody>\r\n<tr>\r\n<td>4. To find [latex]-|p|[\/latex] when [latex]p=-14:[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-|p|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{-14}[\/latex] for p.<\/td>\r\n<td>[latex]-\\mid\\color{red}{-14}\\mid[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]-14[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that the result is negative only when there is a negative sign outside the absolute value symbol.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]144934[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFill in [latex]\\text{&lt; },\\text{ &gt; },\\text {or }=[\/latex] for each of the following:\r\n<ol>\r\n \t<li>[latex]|-5|[\/latex] \u00a0 <strong>___<\/strong>\u00a0 [latex]-|-5|[\/latex]<\/li>\r\n \t<li>[latex]8[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]-|-8|[\/latex]<\/li>\r\n \t<li>[latex]-9[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]- |-9|[\/latex]<\/li>\r\n \t<li>[latex]-|-7|[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]- 7[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"622738\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"622738\"]\r\n\r\nSolution:\r\nTo compare two expressions, simplify each one first. Then compare.\r\n<table id=\"eip-id1166567974475\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|-5|[\/latex]\u00a0 ___\u00a0 [latex]-|-5|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]5[\/latex] ___\u00a0 [latex]- 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Order.<\/td>\r\n<td>[latex]5&gt;-5[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166568580863\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]8[\/latex]\u00a0 ___\u00a0 [latex]-|-8|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]8[\/latex]\u00a0 ___\u00a0 [latex]- 8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Order.<\/td>\r\n<td>[latex]8&gt;-8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166567977584\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-9[\/latex]\u00a0 ___\u00a0 [latex]-|-9|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-9[\/latex]\u00a0 ___\u00a0 [latex]- 9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Order.<\/td>\r\n<td>[latex]-9=-9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166569017628\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-|-7|[\/latex]\u00a0 ___\u00a0 [latex]- 7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-7[\/latex]\u00a0 ___\u00a0 [latex]- 7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Order.<\/td>\r\n<td>[latex]-7=-7[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]144979[\/ohm_question]\r\n\r\n<\/div>\r\nIn the video below we show more examples of how to compare expressions that include absolute value and integers.\r\n\r\nhttps:\/\/youtu.be\/TendEcSaM3w\r\n\r\nAbsolute value bars act like grouping symbols. First simplify inside the absolute value bars as much as possible. Then take the absolute value of the resulting number, and continue with any operations outside the absolute value symbols.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n<ol>\r\n \t<li>[latex]|9 - 3|[\/latex]<\/li>\r\n \t<li>[latex]4|-2|[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"47658\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"47658\"]\r\n\r\nSolution:\r\nFor each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.\r\n<table id=\"eip-id1168466096398\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|9\u22123|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside the absolute value sign.<\/td>\r\n<td>[latex]|6|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469668431\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4|\u22122|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]4(2)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]145007[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]|8+7|-|5+6|[\/latex].\r\n[reveal-answer q=\"743144\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"743144\"]\r\n\r\nSolution:\r\nFor each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.\r\n<table id=\"eip-id1168469785725\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]|8+7|\u2212|5+6|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside each absolute value sign.<\/td>\r\n<td>[latex]|15|\u2212|11|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value of each term.<\/td>\r\n<td>[latex]15\u221211[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]145009[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]24-|19 - 3\\left(6 - 2\\right)|[\/latex]\r\n[reveal-answer q=\"949242\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"949242\"]\r\n\r\nSolution:\r\nWe use the order of operations. Remember to simplify grouping symbols first, so parentheses inside absolute value symbols would be first.\r\n<table id=\"eip-id1168467296922\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]24-|19 - 3\\left(6 - 2\\right)|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify in the parentheses first.<\/td>\r\n<td>[latex]24-|19 - 3\\left(4\\right)|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply [latex]3\\left(4\\right)[\/latex] .<\/td>\r\n<td>[latex]24-|19 - 12|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract inside the absolute value sign.<\/td>\r\n<td>[latex]24-|7|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the absolute value.<\/td>\r\n<td>[latex]24 - 7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]17[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]145010[\/ohm_question]\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">Watch the following video to see more examples of how to simplify expressions that contain absolute value.<\/span>\r\n\r\nhttps:\/\/youtu.be\/cd24nT7mAi0","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use correct notation to indicate absolute value<\/li>\n<li>Simplify expressions that contain\u00a0absolute value<\/li>\n<li>Evaluate expressions that contain absolute value<\/li>\n<\/ul>\n<\/div>\n<p>We saw that numbers such as [latex]5[\/latex] and [latex]-5[\/latex] are opposites because they are the same distance from [latex]0[\/latex] on the number line. They are both five units from [latex]0[\/latex]. The distance between [latex]0[\/latex] and any number on the number line is called the absolute value of that number.<\/p>\n<p>Because distance is never negative, the absolute value of any number is never negative.<\/p>\n<p>The symbol for absolute value is two vertical lines on either side of a number. So the absolute value of [latex]5[\/latex] is written as [latex]|5|[\/latex], and the absolute value of [latex]-5[\/latex] is written as [latex]|-5|[\/latex] as shown below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220135\/CNX_BMath_Figure_03_01_019.png\" alt=\"This figure is a number line. The points negative 5 and 5 are labeled. Above the number line the distance from negative 5 to 0 is labeled as 5 units. Also above the number line the distance from 0 to 5 is labeled as 5 units.\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Absolute Value<\/h3>\n<p>The absolute value of a number is its distance from [latex]0[\/latex] on the number line.<br \/>\nThe absolute value of a number [latex]n[\/latex] is written as [latex]|n|[\/latex].<\/p>\n<p>[latex]|n|\\ge 0[\/latex] for all numbers<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<ol>\n<li>\u00a0[latex]|3|[\/latex]<\/li>\n<li>\u00a0[latex]|-44|[\/latex]<\/li>\n<li>\u00a0[latex]|0|[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<table id=\"eip-id1165118025864\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|3|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex] is [latex]3[\/latex] units from zero.<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1171842979184\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|-44|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\u221244[\/latex] is [latex]44[\/latex] units from zero.<\/td>\n<td>[latex]44[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1171842583307\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|0|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex] is already at zero.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144930\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144930&theme=oea&iframe_resize_id=ohm144930\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144931\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144931&theme=oea&iframe_resize_id=ohm144931\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144932\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144932&theme=oea&iframe_resize_id=ohm144932\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144933\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144933&theme=oea&iframe_resize_id=ohm144933\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the video below we show another example of how to find the absolute value of an integer.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1: Determine the Absolute Value of an Integer\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/I8bTqGmkqGI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>We treat absolute value bars just like we treat parentheses in the order of operations. We simplify the expression inside first.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate:<\/p>\n<ol>\n<li>[latex]|x|\\text{ when }x=-35[\/latex]<\/li>\n<li>[latex]|\\mathit{\\text{-y}}|\\text{ when }y=-20[\/latex]<\/li>\n<li>[latex]-|u|\\text{ when }u=12[\/latex]<\/li>\n<li>[latex]-|p|\\text{ when }p=-14[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q727778\">Show Solution<\/span><\/p>\n<div id=\"q727778\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466007339\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has the absolute value of x. The second row states to substitute negative 35 for x and has the absolute value symbol with negative 35. The third row states to take the absolute value and has 35.\">\n<tbody>\n<tr>\n<td>1. To find [latex]|x|[\/latex] when [latex]x=-35:[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|x|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-35}[\/latex] for x.<\/td>\n<td>[latex]\\mid\\color{red}{-35}\\mid[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]35[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469585161\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has four rows. The first row has the absolute value of y. The second row states to substitute negative 20 for y and has inside of the absolute value symbol a negative sign with negative 20 inside of parentheses. The third row states to simplify and has 20 inside of the absolute value symbol. The fourth row states to take the absolute value and has 20.\">\n<tbody>\n<tr>\n<td>2. To find [latex]|-y|[\/latex] when [latex]y=-20:[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|-y|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-20}[\/latex] for y.<\/td>\n<td>[latex]\\mid-(\\color{red}{-20})\\mid[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]|20|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]20[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466911241\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has a negative sign in front of the absolute value of u. The second row states to substitute 12 for u and has a negative sign in front of the absolute value symbol with 12 on the inside. The third row states to take the absolute value and has negative 12.\">\n<tbody>\n<tr>\n<td>3. To find [latex]-|u|[\/latex] when [latex]u=12:[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-|u|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{12}[\/latex] for u.<\/td>\n<td>[latex]-\\mid\\color{red}{12}\\mid[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]-12[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468381460\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"This figure has three rows. The first row has a negative sign in front of the absolute value of p. The second row states to substitute negative 14 for p and has a negative sign in front of the absolute value of negative 14. The third row states to take the absolute value and has negative 14.\">\n<tbody>\n<tr>\n<td>4. To find [latex]-|p|[\/latex] when [latex]p=-14:[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-|p|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-14}[\/latex] for p.<\/td>\n<td>[latex]-\\mid\\color{red}{-14}\\mid[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]-14[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that the result is negative only when there is a negative sign outside the absolute value symbol.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144934\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144934&theme=oea&iframe_resize_id=ohm144934\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Fill in [latex]\\text{< },\\text{ > },\\text {or }=[\/latex] for each of the following:<\/p>\n<ol>\n<li>[latex]|-5|[\/latex] \u00a0 <strong>___<\/strong>\u00a0 [latex]-|-5|[\/latex]<\/li>\n<li>[latex]8[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]-|-8|[\/latex]<\/li>\n<li>[latex]-9[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]- |-9|[\/latex]<\/li>\n<li>[latex]-|-7|[\/latex]\u00a0 <strong>___<\/strong>\u00a0 [latex]- 7[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q622738\">Show Solution<\/span><\/p>\n<div id=\"q622738\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nTo compare two expressions, simplify each one first. Then compare.<\/p>\n<table id=\"eip-id1166567974475\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|-5|[\/latex]\u00a0 ___\u00a0 [latex]-|-5|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]5[\/latex] ___\u00a0 [latex]- 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Order.<\/td>\n<td>[latex]5>-5[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166568580863\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]8[\/latex]\u00a0 ___\u00a0 [latex]-|-8|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]8[\/latex]\u00a0 ___\u00a0 [latex]- 8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Order.<\/td>\n<td>[latex]8>-8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166567977584\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-9[\/latex]\u00a0 ___\u00a0 [latex]-|-9|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-9[\/latex]\u00a0 ___\u00a0 [latex]- 9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Order.<\/td>\n<td>[latex]-9=-9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166569017628\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-|-7|[\/latex]\u00a0 ___\u00a0 [latex]- 7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-7[\/latex]\u00a0 ___\u00a0 [latex]- 7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Order.<\/td>\n<td>[latex]-7=-7[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144979\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144979&theme=oea&iframe_resize_id=ohm144979\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the video below we show more examples of how to compare expressions that include absolute value and integers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Comparing Absolute Value of Integers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/TendEcSaM3w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Absolute value bars act like grouping symbols. First simplify inside the absolute value bars as much as possible. Then take the absolute value of the resulting number, and continue with any operations outside the absolute value symbols.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<ol>\n<li>[latex]|9 - 3|[\/latex]<\/li>\n<li>[latex]4|-2|[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q47658\">Show Solution<\/span><\/p>\n<div id=\"q47658\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nFor each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.<\/p>\n<table id=\"eip-id1168466096398\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]|9\u22123|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the absolute value sign.<\/td>\n<td>[latex]|6|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469668431\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]4|\u22122|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]4(2)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145007\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145007&theme=oea&iframe_resize_id=ohm145007\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]|8+7|-|5+6|[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q743144\">Show Solution<\/span><\/p>\n<div id=\"q743144\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nFor each expression, follow the order of operations. Begin inside the absolute value symbols just as with parentheses.<\/p>\n<table id=\"eip-id1168469785725\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]|8+7|\u2212|5+6|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside each absolute value sign.<\/td>\n<td>[latex]|15|\u2212|11|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value of each term.<\/td>\n<td>[latex]15\u221211[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145009\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145009&theme=oea&iframe_resize_id=ohm145009\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]24-|19 - 3\\left(6 - 2\\right)|[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q949242\">Show Solution<\/span><\/p>\n<div id=\"q949242\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe use the order of operations. Remember to simplify grouping symbols first, so parentheses inside absolute value symbols would be first.<\/p>\n<table id=\"eip-id1168467296922\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]24-|19 - 3\\left(6 - 2\\right)|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify in the parentheses first.<\/td>\n<td>[latex]24-|19 - 3\\left(4\\right)|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply [latex]3\\left(4\\right)[\/latex] .<\/td>\n<td>[latex]24-|19 - 12|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract inside the absolute value sign.<\/td>\n<td>[latex]24-|7|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>[latex]24 - 7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]17[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145010\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145010&theme=oea&iframe_resize_id=ohm145010&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><span style=\"color: #000000;\">Watch the following video to see more examples of how to simplify expressions that contain absolute value.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Simplify Absolute Value Expressions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/cd24nT7mAi0?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-3564\">\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>Simplify Absolute Value Expressions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/cd24nT7mAi0\">https:\/\/youtu.be\/cd24nT7mAi0<\/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>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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Determine the Absolute Value of an Integer. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/I8bTqGmkqGI\">https:\/\/youtu.be\/I8bTqGmkqGI<\/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: Comparing Absolute Value of Integers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/TendEcSaM3w\">https:\/\/youtu.be\/TendEcSaM3w<\/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>Question ID: 144930, 144931, 144932, 144933, 144934, 144979, 145007, 145009. <strong>Authored by<\/strong>: Alyson Day. <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, 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":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex 1: Determine the Absolute Value of an Integer\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/I8bTqGmkqGI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Comparing Absolute Value of Integers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/TendEcSaM3w\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"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\"},{\"type\":\"original\",\"description\":\"Simplify Absolute Value Expressions\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/cd24nT7mAi0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 144930, 144931, 144932, 144933, 144934, 144979, 145007, 145009\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"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-3564","chapter","type-chapter","status-publish","hentry"],"part":1193,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3564","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3564\/revisions"}],"predecessor-version":[{"id":5675,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3564\/revisions\/5675"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1193"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3564\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3564"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3564"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3564"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}