{"id":3562,"date":"2019-12-31T17:02:49","date_gmt":"2019-12-31T17:02:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3562"},"modified":"2021-02-05T23:48:53","modified_gmt":"2021-02-05T23:48:53","slug":"notation-and-definition-of-the-set-of-integers","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/notation-and-definition-of-the-set-of-integers\/","title":{"raw":"Notation and Definition of the Set of Integers","rendered":"Notation and Definition of the Set of Integers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write the opposite of a given number<\/li>\r\n \t<li>Use correct notation to indicate\u00a0the opposite of a number<\/li>\r\n \t<li>Identify the elements of the set of integers as the counting numbers, their opposites, and zero<\/li>\r\n<\/ul>\r\n<\/div>\r\nOn the number line, the negative numbers are a mirror image of the positive numbers with zero in the middle. Because the numbers [latex]2[\/latex] and [latex]-2[\/latex] are the same distance from zero, they are called opposites. The opposite of [latex]2[\/latex] is [latex]-2[\/latex], and the opposite of [latex]-2[\/latex] is [latex]2[\/latex] as shown in figure(a). Similarly, [latex]3[\/latex] and [latex]-3[\/latex] are opposites as shown in figure(b).\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220126\/CNX_BMath_Figure_03_01_016.png\" alt=\"This figure shows two number lines. The first has points negative 2 and positive 2 labeled. Below the first line the statement is the numbers negative 2 and 2 are opposites. The second number line has the points negative 3 and 3 labeled. Below the number line is the statement negative 3 and 3 are opposites.\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Opposite<\/h3>\r\nThe opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the opposite of each number:\r\n\r\n1. [latex]7[\/latex]\r\n\r\n2. [latex]-10[\/latex]\r\n\r\nSolution:\r\n\r\n1. The number [latex]-7[\/latex] is the same distance from [latex]0[\/latex] as [latex]7[\/latex], but on the opposite side of [latex]0[\/latex]. So [latex]-7[\/latex] is the opposite of [latex]7[\/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\/24220128\/CNX_BMath_Figure_03_01_017.png\" alt=\"This figure is a number line. The points negative 7 and 7 are labeled. Above the line it is shown the distance from 0 to negative 7 and the distance from 0 to 7 are both 7.\" \/>\r\n\r\n2. The number [latex]10[\/latex] is the same distance from [latex]0[\/latex] as [latex]-10[\/latex] , but on the opposite side of [latex]0[\/latex]. So [latex]10[\/latex] is the opposite of [latex]-10[\/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\/24220130\/CNX_BMath_Figure_03_01_018.png\" alt=\"This figure is a number line. The points negative 10 and 10 are labeled. Above the line it is shown the distance from 0 to negative 10 and the distance from 0 to 10 are both 10.\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144926&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144927&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\nThe video below shows more examples of how to find the opposite of an integer.\r\n\r\nhttps:\/\/youtu.be\/suk9KMzOKkU\r\n<h3>Opposite Notation<\/h3>\r\nJust as the same word in English can have different meanings, the same symbol in algebra can have different meanings. The specific meaning becomes clear by looking at how it is used. You have seen the symbol \"[latex]-[\/latex]\" in three different ways.\r\n<table id=\"eip-id1168469523154\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]10 - 4[\/latex]<\/td>\r\n<td>Between two numbers, the symbol indicates the operation of subtraction.We read [latex]10 - 4[\/latex] as 10 <em>minus<\/em> [latex]4[\/latex] .<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-8[\/latex]<\/td>\r\n<td>In front of a number, the symbol indicates a negative number.We read [latex]-8[\/latex] as <em>negative eight<\/em>.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-x[\/latex]<\/td>\r\n<td>In front of a variable or a number, it indicates the opposite.We read [latex]-x[\/latex] as <em>the opposite of<\/em> [latex]x[\/latex] .<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-\\left(-2\\right)[\/latex]<\/td>\r\n<td>Here we have two signs. The sign in the parentheses indicates that the number is negative 2.The sign outside the parentheses indicates the opposite.We read [latex]-\\left(-2\\right)[\/latex] as <em>the opposite of<\/em> [latex]-2[\/latex], which is [latex]2[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n<h3>Opposite Notation<\/h3>\r\n[latex]-a[\/latex] means the opposite of the number [latex]a[\/latex]\r\nThe notation [latex]-a[\/latex] is read <em>the opposite of<\/em> [latex]a[\/latex].\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]-\\left(-6\\right)[\/latex].\r\n[reveal-answer q=\"963673\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"963673\"]\r\n\r\nSolution\r\n<table id=\"eip-id1172095963601\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-\\left(-6\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The opposite of [latex]-6[\/latex] is\r\n[latex]6[\/latex].<\/td>\r\n<td>[latex]6[\/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[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144928&amp;theme=oea&amp;iframe_resize_id=mom3[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Integers<\/h3>\r\nThe set of counting numbers, their opposites, and [latex]0[\/latex] is the set of integers.\r\n<strong>Integers<\/strong> are counting numbers, their opposites, and zero.\r\n\r\n[latex]\\dots{-3,-2,-1,0,1,2,3}\\dots [\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWe must be very careful with the signs when evaluating the opposite of a variable.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate [latex]-x:[\/latex]\r\n\r\n1. When [latex]x=8[\/latex]\r\n2. When [latex]x=-8[\/latex].\r\n[reveal-answer q=\"778361\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"778361\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469610553\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row is negative x. The second row states to substitute 8 for x and shows a negative sign in front of parentheses containing the number 8. The third row states to simplify and shows the number negative 8.\">\r\n<tbody>\r\n<tr style=\"height: 74px\">\r\n<td style=\"height: 74px\">1.To evaluate [latex]-x[\/latex] when [latex]x=8[\/latex] , substitute [latex]8[\/latex] for [latex]x[\/latex] .<\/td>\r\n<td style=\"height: 74px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">\u00a0Substitute [latex]\\color{red}{8}[\/latex] for x.<\/td>\r\n<td style=\"height: 15px\">[latex]-x[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\"><\/td>\r\n<td style=\"height: 30px\">[latex]-(\\color{red}{8})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.0938px\">\r\n<td style=\"height: 15.0938px\">Simplify.<\/td>\r\n<td style=\"height: 15.0938px\">[latex]-8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466251150\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row is negative x. The second row states to substitute negative 8 for x and shows a negative sign in front of parentheses containing the number negative 8. The third row states to simplify and shows the number 8.\">\r\n<tbody>\r\n<tr>\r\n<td>2.To evaluate [latex]-x[\/latex] when [latex]x=-8[\/latex] , substitute [latex]-8[\/latex] for [latex]x[\/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>\u00a0Substitute [latex]\\color{red}{8}[\/latex] for x.<\/td>\r\n<td>[latex]-(\\color{red}{-8})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/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[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144929&amp;theme=oea&amp;iframe_resize_id=mom4[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write the opposite of a given number<\/li>\n<li>Use correct notation to indicate\u00a0the opposite of a number<\/li>\n<li>Identify the elements of the set of integers as the counting numbers, their opposites, and zero<\/li>\n<\/ul>\n<\/div>\n<p>On the number line, the negative numbers are a mirror image of the positive numbers with zero in the middle. Because the numbers [latex]2[\/latex] and [latex]-2[\/latex] are the same distance from zero, they are called opposites. The opposite of [latex]2[\/latex] is [latex]-2[\/latex], and the opposite of [latex]-2[\/latex] is [latex]2[\/latex] as shown in figure(a). Similarly, [latex]3[\/latex] and [latex]-3[\/latex] are opposites as shown in figure(b).<\/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\/24220126\/CNX_BMath_Figure_03_01_016.png\" alt=\"This figure shows two number lines. The first has points negative 2 and positive 2 labeled. Below the first line the statement is the numbers negative 2 and 2 are opposites. The second number line has the points negative 3 and 3 labeled. Below the number line is the statement negative 3 and 3 are opposites.\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Opposite<\/h3>\n<p>The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the opposite of each number:<\/p>\n<p>1. [latex]7[\/latex]<\/p>\n<p>2. [latex]-10[\/latex]<\/p>\n<p>Solution:<\/p>\n<p>1. The number [latex]-7[\/latex] is the same distance from [latex]0[\/latex] as [latex]7[\/latex], but on the opposite side of [latex]0[\/latex]. So [latex]-7[\/latex] is the opposite of [latex]7[\/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\/24220128\/CNX_BMath_Figure_03_01_017.png\" alt=\"This figure is a number line. The points negative 7 and 7 are labeled. Above the line it is shown the distance from 0 to negative 7 and the distance from 0 to 7 are both 7.\" \/><\/p>\n<p>2. The number [latex]10[\/latex] is the same distance from [latex]0[\/latex] as [latex]-10[\/latex] , but on the opposite side of [latex]0[\/latex]. So [latex]10[\/latex] is the opposite of [latex]-10[\/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\/24220130\/CNX_BMath_Figure_03_01_018.png\" alt=\"This figure is a number line. The points negative 10 and 10 are labeled. Above the line it is shown the distance from 0 to negative 10 and the distance from 0 to 10 are both 10.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144926\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144926&#38;theme=oea&#38;iframe_resize_id=ohm144926&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144927\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144927&#38;theme=oea&#38;iframe_resize_id=ohm144927&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The video below shows more examples of how to find the opposite of an integer.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Determine the Opposites of Integers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/suk9KMzOKkU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Opposite Notation<\/h3>\n<p>Just as the same word in English can have different meanings, the same symbol in algebra can have different meanings. The specific meaning becomes clear by looking at how it is used. You have seen the symbol &#8220;[latex]-[\/latex]&#8221; in three different ways.<\/p>\n<table id=\"eip-id1168469523154\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]10 - 4[\/latex]<\/td>\n<td>Between two numbers, the symbol indicates the operation of subtraction.We read [latex]10 - 4[\/latex] as 10 <em>minus<\/em> [latex]4[\/latex] .<\/td>\n<\/tr>\n<tr>\n<td>[latex]-8[\/latex]<\/td>\n<td>In front of a number, the symbol indicates a negative number.We read [latex]-8[\/latex] as <em>negative eight<\/em>.<\/td>\n<\/tr>\n<tr>\n<td>[latex]-x[\/latex]<\/td>\n<td>In front of a variable or a number, it indicates the opposite.We read [latex]-x[\/latex] as <em>the opposite of<\/em> [latex]x[\/latex] .<\/td>\n<\/tr>\n<tr>\n<td>[latex]-\\left(-2\\right)[\/latex]<\/td>\n<td>Here we have two signs. The sign in the parentheses indicates that the number is negative 2.The sign outside the parentheses indicates the opposite.We read [latex]-\\left(-2\\right)[\/latex] as <em>the opposite of<\/em> [latex]-2[\/latex], which is [latex]2[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<h3>Opposite Notation<\/h3>\n<p>[latex]-a[\/latex] means the opposite of the number [latex]a[\/latex]<br \/>\nThe notation [latex]-a[\/latex] is read <em>the opposite of<\/em> [latex]a[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]-\\left(-6\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q963673\">Show Solution<\/span><\/p>\n<div id=\"q963673\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1172095963601\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-\\left(-6\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The opposite of [latex]-6[\/latex] is<br \/>\n[latex]6[\/latex].<\/td>\n<td>[latex]6[\/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=\"ohm144928\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144928&#38;theme=oea&#38;iframe_resize_id=ohm144928&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Integers<\/h3>\n<p>The set of counting numbers, their opposites, and [latex]0[\/latex] is the set of integers.<br \/>\n<strong>Integers<\/strong> are counting numbers, their opposites, and zero.<\/p>\n<p>[latex]\\dots{-3,-2,-1,0,1,2,3}\\dots[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>We must be very careful with the signs when evaluating the opposite of a variable.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]-x:[\/latex]<\/p>\n<p>1. When [latex]x=8[\/latex]<br \/>\n2. When [latex]x=-8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q778361\">Show Solution<\/span><\/p>\n<div id=\"q778361\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469610553\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row is negative x. The second row states to substitute 8 for x and shows a negative sign in front of parentheses containing the number 8. The third row states to simplify and shows the number negative 8.\">\n<tbody>\n<tr style=\"height: 74px\">\n<td style=\"height: 74px\">1.To evaluate [latex]-x[\/latex] when [latex]x=8[\/latex] , substitute [latex]8[\/latex] for [latex]x[\/latex] .<\/td>\n<td style=\"height: 74px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">\u00a0Substitute [latex]\\color{red}{8}[\/latex] for x.<\/td>\n<td style=\"height: 15px\">[latex]-x[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\"><\/td>\n<td style=\"height: 30px\">[latex]-(\\color{red}{8})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.0938px\">\n<td style=\"height: 15.0938px\">Simplify.<\/td>\n<td style=\"height: 15.0938px\">[latex]-8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466251150\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row is negative x. The second row states to substitute negative 8 for x and shows a negative sign in front of parentheses containing the number negative 8. The third row states to simplify and shows the number 8.\">\n<tbody>\n<tr>\n<td>2.To evaluate [latex]-x[\/latex] when [latex]x=-8[\/latex] , substitute [latex]-8[\/latex] for [latex]x[\/latex] .<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>\u00a0Substitute [latex]\\color{red}{8}[\/latex] for x.<\/td>\n<td>[latex]-(\\color{red}{-8})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/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=\"ohm144929\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144929&#38;theme=oea&#38;iframe_resize_id=ohm144929&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/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-3562\">\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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Determine the Opposites of Integers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/suk9KMzOKkU\">https:\/\/youtu.be\/suk9KMzOKkU<\/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: 144926, 144927, 144928, 144929. <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 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