{"id":774,"date":"2019-07-29T23:14:59","date_gmt":"2019-07-29T23:14:59","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/solve-linear-inequalities-3\/"},"modified":"2021-08-31T21:18:41","modified_gmt":"2021-08-31T21:18:41","slug":"solve-linear-inequalities-3","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/solve-linear-inequalities-3\/","title":{"raw":"2.5 Solve Inequalities","rendered":"2.5 Solve Inequalities"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Graph inequalities on the number line<\/li>\n \t<li>Solve inequalities using the Subtraction and Addition Properties of inequality<\/li>\n \t<li>Solve inequalities using the Division and Multiplication Properties of inequality<\/li>\n \t<li>Solve inequalities that require simplification<\/li>\n \t<li>Translate to an inequality and solve<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Graph Inequalities on the Number Line<\/h1>\n<div id=\"fs-id1168345725112\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1168345197716\">Do you remember what it means for a number to be a solution to an equation? A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/p>\n<p id=\"fs-id1168345465826\">What about the solution of an inequality? What number would make the inequality \\(x\\) &gt; \\(3\\) true? Are you thinking, \u2018<em data-effect=\"italics\">x<\/em> could be 4\u2019? That\u2019s correct, but <em data-effect=\"italics\">x<\/em> could be 5 too, or 20, or even 3.001. Any number greater than 3 is a solution to the inequality \\(x\\) &gt; \\(3\\).<\/p>\n<p id=\"fs-id1168345507984\">We show the solutions to the inequality \\(x\\) &gt; \\(3\\) on the number line by shading in all the numbers to the right of 3, to show that all numbers greater than 3 are solutions. Because the number 3 itself is not a solution, we put an open parenthesis at 3. The graph of \\(x\\) &gt; \\(3\\) is shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_001\">(Figure)<\/a>. Please note that the following convention is used: light blue arrows point in the positive direction and dark blue arrows point in the negative direction.<\/p>\n\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality \\(x\\) &gt; \\(3\\) is graphed on this number line.<\/div>\n<span id=\"fs-id1168345484183\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_02_07_001_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1168341909119\">The graph of the inequality \\(x\\ge 3\\) is very much like the graph of \\(x\\) &gt; \\(3\\), but now we need to show that 3 is a solution, too. We do that by putting a bracket at \\(x=3\\), as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_002_img_new\">(Figure)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_002_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality \\(x\\ge 3\\) is graphed on this number line.<\/div>\n<span id=\"fs-id1168345414614\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3 is graphed on the number line, with an open bracket at x equals 3, and a red line extending to the right of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_002_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3 is graphed on the number line, with an open bracket at x equals 3, and a red line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1168345255661\">Notice that the open parentheses symbol, (, shows that the endpoint of the inequality is not included. The open bracket symbol, [, shows that the endpoint is included.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345512685\" data-type=\"problem\">\n<p id=\"fs-id1168345744388\">Graph on the number line:<\/p>\n<p id=\"fs-id1168345273771\"><span class=\"token\">a) <\/span>\\(x\\le 1\\) b) \\(x\\) &lt; \\(5\\) c) \\(x\\) &gt; \\(-1\\)<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1168345723696\" data-type=\"solution\">\n<p style=\"padding-left: 40px;\"><span class=\"token\">a) <\/span>\\(x\\le 1\\)<span data-type=\"newline\">\n<\/span> This means all numbers less than or equal to 1. We shade in all the numbers on the number line to the left of 1 and put a bracket at \\(x=1\\) to show that it is included.<span data-type=\"newline\">\n<\/span> <span id=\"fs-id1168345274106\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_003_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">b) <\/span>\\(x\\) &lt; \\(5\\)<span data-type=\"newline\">\n<\/span> This means all numbers less than 5, but not including 5. We shade in all the numbers on the number line to the left of 5 and put a parenthesis at \\(x=5\\) to show it is not included.<span data-type=\"newline\">\n<\/span> <span id=\"fs-id1168345408217\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 5 is graphed on the number line, with an open parenthesis at x equals 5, and a red line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_004_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 5 is graphed on the number line, with an open parenthesis at x equals 5, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">c) <\/span>\\(x\\) &gt; \\(-1\\)<span data-type=\"newline\">\n<\/span> This means all numbers greater than \\(-1\\), but not including \\(-1\\). We shade in all the numbers on the number line to the right of \\(-1\\), then put a parenthesis at \\(x=-1\\) to show it is not included.<span data-type=\"newline\">\n<\/span> <span id=\"fs-id1168345452718\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 1 is graphed on the number line, with an open parenthesis at x equals negative 1, and a red line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_005_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 1 is graphed on the number line, with an open parenthesis at x equals negative 1, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345443645\" data-type=\"problem\">\n<p id=\"fs-id1168345557090\">Graph on the number line: a) \\(x\\le -1\\) b) \\(x\\) &gt;\u00a0\\(2\\) c) \\(x\\) &lt; \\(3\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345434561\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">a)\n<\/span><span data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the left of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_006_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">b)\n<\/span><span id=\"fs-id1168345622953\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_007_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">c)\n<\/span><span id=\"fs-id1168345687655\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the left of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_008_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345250830\">We can also represent inequalities using <em data-effect=\"italics\">interval notation.<\/em> As we saw above, the inequality \\(x\\) &gt; \\(3\\) means all numbers greater than 3. There is no upper end to the solution to this inequality. In <span class=\"no-emphasis\" data-type=\"term\">interval notation<\/span>, we express \\(x\\) &gt; \\(3\\) as \\(\\left(3,\\infty \\right).\\) The symbol \\(\\infty \\) is read as \u2018infinity\u2019. It is not an actual number. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_012_img_new\">(Figure)<\/a> shows both the number line and the interval notation.<\/p>\n\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_012_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality \\(x\\) &gt; \\(3\\) is graphed on this number line and written in interval notation.<\/div>\n<span data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 3 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_012_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1168345456146\">The inequality \\(x\\le 1\\) means all numbers less than or equal to 1. There is no lower end to those numbers. We write \\(x\\le 1\\) in interval notation as \\(\\left(-\\infty ,1\\right]\\). The symbol \\(-\\infty \\) is read as \u2018negative infinity\u2019. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_013_img_new\">(Figure)<\/a> shows both the number line and interval notation.<\/p>\n\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_013_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality \\(x\\le 1\\) is graphed on this number line and written in interval notation.<\/div>\n<span id=\"fs-id1168345241928\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 1, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_013_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 1, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div data-type=\"note\">\n<div data-type=\"title\">Inequalities, Number Lines, and Interval Notation<\/div>\n<span id=\"fs-id1168345291600\" data-type=\"media\" data-alt=\"This figure show four number lines, all without tick marks. The inequality x is greater than a is graphed on the first number line, with an open parenthesis at x equals a, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, a comma infinity, parenthesis. The inequality x is greater than or equal to a is graphed on the second number line, with an open bracket at x equals a, and a red line extending to the right of the bracket. The inequality is also written in interval notation as bracket, a comma infinity, parenthesis. The inequality x is less than a is graphed on the third number line, with an open parenthesis at x equals a, and a red line extending to the left of the parenthesis. The inequality is also written in interval notation as parenthesis, negative infinity comma a, parenthesis. The inequality x is less than or equal to a is graphed on the last number line, with an open bracket at x equals a, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma a, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_014_img_new.jpg\" alt=\"This figure show four number lines, all without tick marks. The inequality x is greater than a is graphed on the first number line, with an open parenthesis at x equals a, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, a comma infinity, parenthesis. The inequality x is greater than or equal to a is graphed on the second number line, with an open bracket at x equals a, and a red line extending to the right of the bracket. The inequality is also written in interval notation as bracket, a comma infinity, parenthesis. The inequality x is less than a is graphed on the third number line, with an open parenthesis at x equals a, and a red line extending to the left of the parenthesis. The inequality is also written in interval notation as parenthesis, negative infinity comma a, parenthesis. The inequality x is less than or equal to a is graphed on the last number line, with an open bracket at x equals a, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma a, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\nDid you notice how the parenthesis or bracket in the interval notation matches the symbol at the endpoint of the arrow? These relationships are shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_015_img_new\">(Figure)<\/a>.\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_015_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The notation for inequalities on a number line and in interval notation use similar symbols to express the endpoints of intervals.<\/div>\n<span id=\"fs-id1168345623160\" data-type=\"media\" data-alt=\"This figure shows the same four number lines as above, with the same interval notation labels. Below the interval notation for each number line, there is text indicating how the notation on the number lines is similar to the interval notation. The first number line is a graph of x is greater than a, and the interval notation is parenthesis, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left parenthesis.\u201d The second number line is a graph of x is greater than or equal to a, and the interval notation is bracket, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left bracket.\u201d The third number line is a graph of x is less than a, and the interval notation is parenthesis, negative infinity comma a, parenthesis. The text below reads: \u201cBoth have a right parenthesis.\u201d The last number line is a graph of x is less than or equal to a, and the interval notation is parenthesis, negative infinity comma a, bracket. The text below reads: \u201cBoth have a right bracket.\u201d\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_015_img_new.jpg\" alt=\"This figure shows the same four number lines as above, with the same interval notation labels. Below the interval notation for each number line, there is text indicating how the notation on the number lines is similar to the interval notation. The first number line is a graph of x is greater than a, and the interval notation is parenthesis, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left parenthesis.\u201d The second number line is a graph of x is greater than or equal to a, and the interval notation is bracket, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left bracket.\u201d The third number line is a graph of x is less than a, and the interval notation is parenthesis, negative infinity comma a, parenthesis. The text below reads: \u201cBoth have a right parenthesis.\u201d The last number line is a graph of x is less than or equal to a, and the interval notation is parenthesis, negative infinity comma a, bracket. The text below reads: \u201cBoth have a right bracket.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345239191\" data-type=\"problem\">\n<p id=\"fs-id1168341847896\">Graph on the number line and write in interval notation.<\/p>\n<p id=\"fs-id1168345550454\"><span class=\"token\">a) <\/span>\\(x\\ge -3\\) b) \\(x\\) &lt; \\(2.5\\) c) \\(x\\le -\\frac{3}{5}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345453189\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<span class=\"token\">a)<\/span><span data-type=\"newline\">\n<\/span>\n<table id=\"eip-id1168465214382\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is greater than or equal to negative 3. One line down on the left, the instructions say: \u201cShade to the right of negative 3, and put a bracket at negative 3.\u201d To the right of this sentence is a number line ranging from negative 4 to negative 1, with tick marks at each integer. There is a bracket at negative 3 and a red line extends to the right from negative 3. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: bracket, negative 3 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465214399\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the right of \\(-3\\), and put a bracket at \\(-3\\).<\/td>\n<td><span id=\"eip-id1168465214426\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168465214443\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<span data-type=\"newline\">b)<\/span>\n<table id=\"eip-id1168463870324\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is less than 2.5. One line down on the left, the instructions say: \u201cShade to the left of 2.5, and put a parenthesis at 2.5.\u201d To the right of this sentence is a number line ranging from 0 to 3, with tick marks at each integer. There is a parenthesis at 2.5 (written in) and a red line extends to the left from 2.5. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: parenthesis, negative infinity comma 2.5, parethesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463870342\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the left of \\(2.5\\), and put a parenthesis at \\(2.5\\).<\/td>\n<td><span id=\"eip-id1168463870368\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463870385\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<span data-type=\"newline\">c)<\/span>\n<table id=\"eip-id1168465191280\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is less than or equal to negative 3\/5. One line down on the left, the instructions say: \u201cShade to the left of negative 3\/5, and put a bracket at negative 3\/5.\u201d To the right of this sentence is a number line ranging from negative 2 to 1, with tick marks at each integer. There is a bracket at negative 3\/5 (written in) and a red line extends to the left from negative 3\/5. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: parenthesis, negative infinity comma negative three fifths, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465191297\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the left of \\(-\\frac{3}{5}\\), and put a bracket at \\(-\\frac{3}{5}\\).<\/td>\n<td><span id=\"eip-id1168465191334\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168465191352\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345420817\" data-type=\"problem\">\n<p id=\"fs-id1168345407937\">Graph on the number line and write in interval notation:<\/p>\n<p id=\"fs-id1168345297606\"><span class=\"token\">a) <\/span>\\(x\\) &gt; \\(2\\) b) \\(x\\le -1.5\\)c)\u00a0 \\(x\\ge \\frac{3}{4}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345291328\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p style=\"padding-left: 40px;\"><span class=\"token\">a)<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345448172\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 2 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_019_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 2 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">b)<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345579989\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 1.5, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_020_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 1.5, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">c)<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345435633\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3\/4 is graphed on the number line, with an open bracket at x equals 3\/4, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 3\/4 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_021_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3\/4 is graphed on the number line, with an open bracket at x equals 3\/4, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 3\/4 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345517735\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Solve Inequalities using the Subtraction and Addition Properties of Inequality<\/h1>\n<p id=\"fs-id1168345293507\">The Subtraction and Addition Properties of Equality state that if two quantities are equal, when we add or subtract the same amount from both quantities, the results will be equal.<\/p>\n\n<div id=\"fs-id1168345241070\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Equality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\(\\begin{array}{cccc}\\mathbf{\\text{Subtraction Property of Equality}}\\hfill &amp; &amp; &amp; \\mathbf{\\text{Addition Property of Equality}}\\hfill \\\\ \\text{For any numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\hfill &amp; &amp; &amp; \\text{For any numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\hfill \\\\ \\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill a-c&amp; =\\hfill &amp; b-c.\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill a+c&amp; =\\hfill &amp; b+c.\\hfill \\end{array}\\hfill \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345630854\">Similar properties hold true for inequalities.<\/p>\n\n<table id=\"eip-id1168461203088\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cFor example, we know that negative 4 is less than 2.\u201d To the right of this instruction is the inequality negative 4 is less than 2. One line down on the left, the instructions say: \u201cIf we subtract 5 from both quantities, is the left side still less than the right side?\u201d To the right of this instruction is the original inequality with 5 subtracted from both sides: negative 4 minus 5 question mark 2 minus 5. Another line down on the left, the instructions say: \u201cWe get negative 9 on the left and negative 3 on the right.\u201d To the right of this sentence is the line negative 9 question mark negative 3. Another line down on the left, the instructions say: \u201cAnd we know negative 9 is less then negative 3.\u201d To the right of this sentence is the inequality negative 9 is less than negative 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td>For example, we know that \u22124 is less than 2.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203102\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>If we subtract 5 from both quantities, is the<span data-type=\"newline\">\n<\/span>left side still less than the right side?<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203119\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We get \u22129 on the left and \u22123 on the right.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203136\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>And we know \u22129 is less than \u22123.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203154\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><strong data-effect=\"bold\">The inequality sign stayed the same.<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345216274\">Similarly we could show that the inequality also stays the same for addition.<\/p>\n<p id=\"fs-id1168345408152\">This leads us to the Subtraction and Addition Properties of Inequality.<\/p>\n\n<div data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Inequality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n<img class=\"alignnone size-full wp-image-6410\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.39.52-PM.png\" alt=\"\" width=\"2384\" height=\"722\">\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345277860\">We use these properties to solve inequalities, taking the same steps we used to solve equations. Solving the inequality \\(x+5\\) &gt; \\(9\\), the steps would look like this:<\/p>\n\n<table id=\"eip-608\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(x+5\\) &gt; \\(9\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides to isolate \\(x\\).<\/td>\n<td>\\(x+5-5\\) &gt; \\(9-5\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(x\\) &gt; \\(4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345742500\">Any number greater than 4 is a solution to this inequality.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345328196\" data-type=\"problem\">\n<p id=\"fs-id1168345215094\">Solve the inequality \\(n-\\frac{1}{2}\\le \\frac{5}{8}\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345429191\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461308445\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality n minus \u00bd is less than or equal to 5\/8. One line down on the left, the instructions say: \u201cAdd \u00bd to both sides of the inequality.\u201d To the right of this instruction is the same inequality with \u00bd added to both sides: n minus \u00bd plus \u00bd is less than or equal to 5\/8 plus \u00bd. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the inequality n is less than or equal to 9\/8. One more line down on the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from 0 to 3 with n is less than or equal to 9\/8 graphed on it. There is a bracket at n equals 9\/8, and a red line extends to the left from 9\/8. Another line down on the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the interval notation for the graph: parenthesis, negative infinity comma 9\/8, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168461308479\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add \\(\\frac{1}{2}\\) to both sides of the inequality.<\/td>\n<td><span id=\"eip-id1168461308504\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461308521\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461308538\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168461308555\" data-type=\"media\" data-alt=\".\"><img src=\"CNX_ElemAlg_Figure_02_07_026e_img_new.jpg#fixme#fixme#fixme\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345454848\" data-type=\"problem\">\n<p id=\"fs-id1168345559943\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345429017\">\\(p-\\frac{3}{4}\\ge \\frac{1}{6}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168341901859\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168345256519\" data-type=\"media\" data-alt=\"This figure shows the inequality p is greater than or equal to 11\/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at p equals 11\/12, and a dark line extends to the right from 11\/12. Below the number line is the solution written in interval notation: bracket, 11\/12 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_027_img_new.jpg\" alt=\"This figure shows the inequality p is greater than or equal to 11\/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at p equals 11\/12, and a dark line extends to the right from 11\/12. Below the number line is the solution written in interval notation: bracket, 11\/12 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n&nbsp;\n<div id=\"fs-id1168345292080\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345644774\" data-type=\"exercise\">\n<div id=\"fs-id1168345454848\" data-type=\"problem\">\u00a0<span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif; font-size: 1.2em; font-weight: bold;\">Solve Inequalities using the Division and Multiplication Properties of Inequality<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345667361\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1168341853058\">The Division and Multiplication Properties of Equality state that if two quantities are equal, when we divide or multiply both quantities by the same amount, the results will also be equal (provided we don\u2019t divide by 0).<\/p>\n\n<div id=\"fs-id1168345278408\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Equality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\(\\begin{array}{cccc}\\mathbf{\\text{Division Property of Equality}}\\hfill &amp; &amp; &amp; \\mathbf{\\text{Multiplication Property of Equality}}\\hfill \\\\ \\text{For any numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,c,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\ne 0,\\hfill &amp; &amp; &amp; \\text{For any real numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,c,\\hfill \\\\ \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; a\\hfill &amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\frac{a}{c}\\hfill &amp; =\\hfill &amp; \\frac{b}{c}.\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; a\\hfill &amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; ac\\hfill &amp; =\\hfill &amp; bc.\\hfill \\end{array}\\hfill \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168341857701\">Are there similar properties for inequalities? What happens to an inequality when we divide or multiply both sides by a constant?<\/p>\n<p id=\"fs-id1168345223956\">Consider some numerical examples.<\/p>\n\n<table id=\"eip-id1168463786734\" summary=\"This figure shows the results of dividing and multiplying an inequality by the same constant. The figure has four columns, with written instructions in the first and third columns, and math in the second and fourth columns. At the top of the figure, the inequality 10 is less than 15 appears at the top of the second and fourth columns. One line down the left, the instructions say: \u201cDivide both sides by 5.\u201d To the right of this sentence is the inequality divided by 5 on both sides: 10 over 5 question mark 15 over 5. To the right of this is the instruction: \u201cMultiply both sides by 5.\u201d To the right of this is the original inequality multiplied by 5 on both sides: 10 times 5 question mark 15 times 5. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the line 2 question mark 3. The third column is blank here. In the fourth column is the line 50 question mark 75. Another line down to the left, the instructions say: \u201cFill in the inequality signs.\u201d To the right of this sentence is the inequality 2 is less than 3. The third column is blank here. In the fourth column is the inequality 50 is less than 75.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463749570\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461145237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 5.<\/td>\n<td><span id=\"eip-id1168461145254\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td>Multiply both sides by 5.<\/td>\n<td><span id=\"eip-id1168461145268\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463992619\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168463992633\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Fill in the inequality signs.<\/td>\n<td><span id=\"eip-id1168463992650\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168464056892\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1171792354443\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\mathbf{\\text{The inequality signs stayed the same.}}\\)<\/div>\n<p id=\"fs-id1168345389883\">Does the inequality stay the same when we divide or multiply by a negative number?<\/p>\n\n<table id=\"eip-id1168463765216\" class=\"unnumbered unstyled\" summary=\"This figure shows the results of dividing and multiplying an inequality by the same negative constant. The figure has four columns, with written instructions in the first and third columns, and math in the second and fourth columns. At the top of the figure, the inequality 10 is less than 15 appears at the top of the second and fourth columns. One line down the left, the instructions say: \u201cDivide both sides by negative 5.\u201d To the right of this sentence is the inequality divided by negative 5 on both sides: 10 over negative 5 question mark 15 over negative 5. To the right of this is the instruction: \u201cMultiply both sides by negative 5.\u201d To the right of this is the original inequality multiplied by negative 5 on both sides: 10 times negative 5 question mark 15 times negative 5. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the line negative 2 question mark negative 3. The third column is blank here. In the fourth column is the line negative 50 question mark negative 75. Another line down to the left, the instructions say: \u201cFill in the inequality signs.\u201d To the right of this sentence is the inequality negative 2 is greater than negative 3. The third column is blank here. In the fourth column is the inequality negative 50 is greater than negative 75.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168464590083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461229936\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by \u22125.<\/td>\n<td><span id=\"eip-id1168461229953\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td>Multiply both sides by \u22125.<\/td>\n<td><span id=\"eip-id1168463888075\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463888091\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461292100\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Fill in the inequality signs.<\/td>\n<td><span id=\"eip-id1168461292116\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168463779381\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1171792498411\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\mathbf{\\text{The inequality signs reversed their direction.}}\\)<\/div>\n<p id=\"fs-id1168345261900\">When we divide or multiply an inequality by a positive number, the inequality sign stays the same. When we divide or multiply an inequality by a negative number, the inequality sign reverses.<\/p>\n<p id=\"fs-id1168345297633\">Here are the Division and Multiplication Properties of Inequality for easy reference.<\/p>\n\n<div id=\"fs-id1168345450893\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Division and Multiplication Properties of Inequality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n<img class=\"alignnone size-full wp-image-6411\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.40.23-PM.png\" alt=\"\" width=\"1956\" height=\"1148\">\n\n<\/div>\n<\/div>\n<span style=\"text-align: initial; font-size: 14pt;\">When we <\/span><strong style=\"text-align: initial; font-size: 14pt;\" data-effect=\"bold\">divide or multiply<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> an inequality by a:<\/span>\n\n<\/div>\n<\/div>\n<ul id=\"fs-id1168341864334\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">positive<\/strong> number, the inequality stays the <strong data-effect=\"bold\">same<\/strong>.<\/li>\n \t<li><strong data-effect=\"bold\">negative<\/strong> number, the inequality <strong data-effect=\"bold\">reverses<\/strong>.<\/li>\n<\/ul>\n<div id=\"fs-id1168345251297\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345292807\" data-type=\"exercise\">\n<div id=\"fs-id1168345526626\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345450214\" data-type=\"problem\">\n<p id=\"fs-id1168345284577\">Solve the inequality \\(7y\\) &lt; \\(42\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345692782\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168465351020\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 7y is less than 42. One line down to the left, the instructions say: \u201cDivide both sides of the inequality by 7. Since 7 is greater than 0, the inequality stays the same.\u201d To the right of this instruction is the original inequality divided by 7 on both sides: 7y over 7 is less than 42 over 7. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality y is less than 6. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from 4 to 7, with tick marks at each integer. The inequality y is less than 6 is graphed on the number line, with an open parenthesis at y equals 6, and a red line extending from there to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma 6, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465351054\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Divide both sides of the inequality by 7.<span data-type=\"newline\">\n<\/span>Since \\(7\\) &gt; \\(0\\), the inequality stays the same.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168465351071\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465089167\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168465089185\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168465089202\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345526626\" data-type=\"problem\">\n<p id=\"fs-id1168345297541\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345522080\">\\(\\left(8,\\infty \\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345474658\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345743063\">\\(c\\) &gt; \\(8\\)<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1168345388293\" data-type=\"media\" data-alt=\"This figure is a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is greater than 8 is graphed on the number line, with an open parenthesis at c equals 8, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_032_img_new.jpg\" alt=\"This figure is a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is greater than 8 is graphed on the number line, with an open parenthesis at c equals 8, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345287560\" data-type=\"problem\">\n<p id=\"fs-id1168345455350\">Solve the inequality \\(-10a\\ge 50\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1168345422084\" data-type=\"solution\">\n<table id=\"eip-id1168460536424\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality negative 10a is greater than or equal to 50. One line down to the left, the instructions say: \u201cDivide both sides of the inequality by negative 10. Since negative 10 is less than 0, the inequality reverses.\u201d To the right of this instruction is the original inequality divided by negative 10 on both sides: negative 10a over negative 10 is greater than or equal to 50 over negative 10, with the greater than or equal to sign written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality a is less than or equal to negative 5. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 7 to negative 4, with tick marks at each integer. The inequality a is less then or equal to negative 5 is graphed on the number line, with an open bracket at a equals negative 5, and a red line extending from there to the left. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma negative 5, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168460536420\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Divide both sides of the inequality by \u221210.<span data-type=\"newline\">\n<\/span>Since \\(-10\\) &lt; \\(0\\), the inequality reverses.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168462716164\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168462716199\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168462716216\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168462716233\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342181668\" data-type=\"problem\">\n<p id=\"fs-id1168342181516\">Solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168342040546\">\\(-8q\\) &lt; \\(32\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345388596\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345250203\">\\(q\\) &gt; \\(-4\\)<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1168345250204\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 6 to negative 3 with tick marks for each integer. The inequality q is greater than negative 4 is graphed on the number line, with an open parenthesis at q equals negative 4, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 4 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_035_img_new.jpg\" alt=\"This figure is a number line ranging from negative 6 to negative 3 with tick marks for each integer. The inequality q is greater than negative 4 is graphed on the number line, with an open parenthesis at q equals negative 4, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 4 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345196580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345644359\" data-type=\"exercise\">\n<h1>Solving Inequalities<\/h1>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345695536\" data-type=\"note\">\n<p id=\"fs-id1168345622665\">Sometimes when solving an inequality, the variable ends up on the right. We can rewrite the inequality in reverse to get the variable to the left.<\/p>\n\n<div data-type=\"equation\" data-label=\"\"><img class=\"wp-image-6412 alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.40.44-PM.png\" alt=\"\" width=\"369\" height=\"29\"><\/div>\n&nbsp;\n<p id=\"fs-id1168342156004\">Think about it as \u201cIf Xavier is taller than Alex, then Alex is shorter than Xavier.\u201d<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345424531\" data-type=\"problem\">\n<p id=\"fs-id1168345500479\">Solve the inequality \\(-20\\) &lt; \\(\\frac{4}{5}u\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345461433\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168462821337\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality negative 20 is less than four-fifths u. One line down to the left, the instructions say: \u201cMultiply both sides of the inequality by 5\/4. Since 5\/4 is greater than 0, the inequality stays the same.\u201d To the right of this instruction is the original inequality multiplied by 5\/4 on both sides: 5\/4 times negative 20 is less than 5\/4 times four-fifths u. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality negative 25 is less than u. One more line down on the left, the instructions say: \u201cRewrite with the variable on the left.\u201d To the right of this sentence is the inequality u is greater than negative 25. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 26 to negative 23, with tick marks at each integer. The inequality u is greater than negative 25 is graphed on the number line, with an open parenthesis at u equals negative 25, and a red line extending from there to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative 25 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168462821374\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Multiply both sides of the inequality by \\(\\frac{5}{4}\\).<span data-type=\"newline\">\n<\/span>Since \\(\\frac{5}{4}\\)&gt; \\(0\\), the inequality stays the same.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168462821398\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168462821436\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the variable on the left.<\/td>\n<td><span id=\"eip-id1168462821453\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168462821471\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168462821488\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345742335\" data-type=\"problem\">\n<p id=\"fs-id1168345742481\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345431017\">\\(24\\le \\frac{3}{8}m\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345676986\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168345527811\" data-type=\"media\" data-alt=\"This figure shows the inequality m is greater than or equal to 64. Below this inequality is a number line ranging from 63 to 67 with tick marks for each integer. The inequality m is greater than or equal to 64 is graphed on the number line, with an open bracket at m equals 64, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 64 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_038_img_new.jpg\" alt=\"This figure shows the inequality m is greater than or equal to 64. Below this inequality is a number line ranging from 63 to 67 with tick marks for each integer. The inequality m is greater than or equal to 64 is graphed on the number line, with an open bracket at m equals 64, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 64 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345483994\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345418989\" data-type=\"exercise\">\n<div id=\"fs-id1168345655058\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345256384\" data-type=\"problem\">\n<p id=\"fs-id1168345448052\">Solve the inequality \\(\\frac{t}{-2}\\ge 8\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345427063\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168460952556\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality t over negative 2 is greater than or equal two 8. One line down to the left, the instructions say: \u201cMultiply both sides of the inequality by negative 2. Since negative 2 is less than 0, the inequality reverses.\u201d To the right of this instruction is the original inequality multiplied by negative 2 on both sides: negative 2 times t over negative 2, with t over negative 2 in parentheses, is less than or equal to negative 2 times 8, with the is less than or equal to symbol written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality t is less than or equal to negative 16. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 18 to negative 15, with tick marks at each integer. The inequality t is less than or equal to negative 16 is graphed on the number line, with an open bracket at t equals negative 16, and a red line extending from the bracket to the left. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma negative 16, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463908074\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Multiply both sides of the inequality by \\(-2\\).<span data-type=\"newline\">\n<\/span>Since \\(-2\\) &lt; \\(0\\), the inequality reverses.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168463908095\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461208480\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461208497\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168461555572\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345508568\" data-type=\"problem\">\n<p id=\"fs-id1168345508570\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1167265668550\">\\(\\frac{k}{-12}\\le 15\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1168345655073\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168345449801\" data-type=\"media\" data-alt=\"This figure shows the inequality k is greater than or equal to negative 180. Below this inequality is a number line ranging from negative 181 to negative 177 with tick marks for each integer. The inequality k is greater than or equal to negative 180 is graphed on the number line, with an open bracket at n equals negative 180, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, negative 180 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_041_img_new.jpg\" alt=\"This figure shows the inequality k is greater than or equal to negative 180. Below this inequality is a number line ranging from negative 181 to negative 177 with tick marks for each integer. The inequality k is greater than or equal to negative 180 is graphed on the number line, with an open bracket at n equals negative 180, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, negative 180 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341960485\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Solve Inequalities That Require Simplification<\/h1>\n<p id=\"fs-id1168345398559\">Most inequalities will take more than one step to solve. We follow the same steps we used in the general strategy for solving linear equations, but be sure to pay close attention during multiplication or division.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345436018\" data-type=\"problem\">\n<p id=\"fs-id1168345436021\">Solve the inequality \\(4m\\le 9m+17\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345287544\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168465372853\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 4m is less than or equal to 9m plus 17. One line down to the left, the instructions say: \u201cSubtract 9m from both sides to collect the variables on the left.\u201d To the right of this sentence is the original inequality with 9m subtracted from both sides: 4m minus 9m is less than or equal to 9m minus 9m plus 17. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality negative 5m is less than or equal to 17. Another line down on the left, the instructions say: \u201cDivide both sides of the inequality by negative 5, and reverse the inequality.\u201d To the right of this instruction is the original inequality divided by negative 5 on both sides: negative 5m over negative 5 is greater than or equal to 17 over negative 5, with the is greater than or equal to symbol written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality m is greater than or equal to negative 17\/5. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 5 to negative 2, with tick marks at each integer. The inequality m is greater than or equal to negative 17\/5 is graphed on the number line, with an open bracket at m equals negative 17\/5 (written in), and a red line extending from the bracket to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: bracket, negative 17\/5 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465372838\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(9m\\) from both sides to collect the variables on the left.<\/td>\n<td><span id=\"eip-id1168465372882\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465372899\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides of the inequality by \u22125, and reverse the inequality.<\/td>\n<td><span id=\"eip-id1168465372917\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465372934\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"fs-id1169145576659\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168465372951\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345374096\" data-type=\"problem\">\n<p id=\"fs-id1168345374098\">Solve the inequality \\(3q\\text{\\hspace{0.17em}}\\ge \\text{\\hspace{0.17em}}7q\\text{\\hspace{0.17em}}-\\text{\\hspace{0.17em}}23\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345446027\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168345255758\" data-type=\"media\" data-alt=\"This figure shows the inequality q is less than or equal to 23\/4. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality q is less than or equal to 23\/4 is graphed on the number line, with an open bracket at q equals 23\/4 (written in), and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 23\/4, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_044_img_new.jpg\" alt=\"This figure shows the inequality q is less than or equal to 23\/4. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality q is less than or equal to 23\/4 is graphed on the number line, with an open bracket at q equals 23\/4 (written in), and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 23\/4, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345325808\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345433462\" data-type=\"exercise\">\n<div id=\"fs-id1168345552417\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345416793\" data-type=\"problem\">\n<p id=\"fs-id1168345385584\">Solve the inequality \\(8p+3\\left(p-12\\right)\\) &gt; \\(7p-28\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168341892598\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461313752\" style=\"height: 244px; width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 8p plus 3 times p minus 12, with p minus 12 in parentheses, is greater than 7p minus 28. One line down to the left, the instructions say: \u201cSimplify each side as much as possible. Distribute.\u201d To the right of this instruction is the inequality with 3 distributed through the parentheses: 8p plus 3p minus 36 is greater than 7p minus 28. One more line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 11p minus 36 is greater than 7p minus 28. Another line down on the left, the instructions say: \u201cSubtract 7p from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 7p subtracted from both sides: 11p minus 36 minus 7p is greater than 7p minus 28 minus 7p. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality 4p minus 36 is greater than negative 28. Another line down on the left, the instructions say: \u201cAdd 36 to both sides to collect the constants on the right.\u201d To the right of this sentence is the same inequality with 36 added to both sides: 4p minus 36 plus 36 is greater than negative 28 plus 36. Another line down on the left, the instructions say: \u201cSimpify.\u201d To the right of this instruction is the inequality 4p is greater than 8. One more line down on the left, the instructions say: \u201cDivide both sides of the inequality by 4; the inequality stays the same.\u201d To the right of this instruction is the inequality divided by 4 on both sides: 4p over 4 is greater than 8 over 4. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality p is greater than 2. Another line down to the left, the instructions say: \u201cGraph the solution on the number line. Write the solution in interval notation.\u201d To the right of this instruction is a number line ranging from 0 to 3, with tick marks at each integer. The inequality p is greater than 2 is graphed on the number line, with an open parenthesis at p equals 2, and a red line extending from the parenthesis to the right. Below the number line is the notation: parenthesis, 2 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify each side as much as possible.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(8p+3\\left(p-12\\right)\\) &gt; \\(7p-28\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Distribute.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{0.6em}{0ex}}8p+3p-36\\) &gt; \\(7p-28\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Combine like terms.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{2.3em}{0ex}}11p-36\\) &gt; \\(7p-28\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Subtract \\(7p\\) from both sides to collect the variables on the left.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{2.2em}{0ex}}11p-36-7p\\) &gt; \\(7p-28-7p\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{1.2em}{0ex}}4p-36\\) &gt; \\(-28\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Add 36 to both sides to collect the constants on the right.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{1.3em}{0ex}}4p-36+36\\) &gt; \\(-28+36\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{2em}{0ex}}4p\\) &gt; \\(8\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Divide both sides of the inequality by 4; the inequality stays the same.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{2em}{0ex}}\\frac{4p}{4}\\) &gt; \\(\\frac{8}{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(\\phantom{\\rule{2.5em}{0ex}}p\\) &gt; \\(2\\)<\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"height: 40px; width: 369.406px;\">Graph the solution on the number line.<\/td>\n<td style=\"height: 40px; width: 308.406px;\"><span id=\"eip-id1168463856754\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_046a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Write the solution in interal notation.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\">\\(\\left(2,\\infty \\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345455047\" data-type=\"problem\">\n<p id=\"fs-id1168345455049\">Solve the inequality \\(9y+2\\left(y+6\\right)\\) &gt; \\(5y-24\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345742714\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168342181624\" data-type=\"media\" data-alt=\"This figure shows the inequality y is greater than negative 6. Below this inequality is a number line ranging from negative 7 to negative 3 with tick marks for each integer. The inequality y is greater than negative 6 is graphed on the number line, with an open parenthesis at y equals negative 6, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 6 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_047_img_new.jpg\" alt=\"This figure shows the inequality y is greater than negative 6. Below this inequality is a number line ranging from negative 7 to negative 3 with tick marks for each integer. The inequality y is greater than negative 6 is graphed on the number line, with an open parenthesis at y equals negative 6, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 6 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<span style=\"text-align: initial; font-size: 14pt;\">Just like some equations are identities and some are contradictions, inequalities may be identities or contradictions, too. We recognize these forms when we are left with only constants as we solve the inequality. If the result is a true statement, we have an identity. If the result is a false statement, we have a contradiction.<\/span>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345387524\" data-type=\"problem\">\n<p id=\"fs-id1168345449878\">Solve the inequality \\(8x-2\\left(5-x\\right)\\) &lt; \\(4\\left(x+9\\right)+6x\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345744775\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461237712\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 8x minus 2 times 5 minus x, with 5 minus x in parentheses, is less than 4 times x plus 9, with x plus 9 in parentheses, plus 6x. One line down to the left, the instructions say: \u201cSimplify each side as much as possible. Distribute.\u201d To the right of this instruction is the inequality with 2 distributed through the parentheses on the left side and 4 distributed through the parentheses on the right: 8x minus 10 plus 2x is less than 4x plus 36 plus 6x. One more line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 10x minus 10 is less than 10x plus 36. Another line down on the left, the instructions say: \u201cSubtract 10x from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 10x subtracted from both sides: 10x minus 10 minus 10x is less than 10x plus 36 minus 10x. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality negative 10 is less than 36. Another line down on the left, the instructions say: \u201cThe x\u2019s are gone, and we have a true statement.\u201d To the right is the text: \u201cThe inequality is an identity. The solution is all real numbers.\u201d Another line down to the left, the instructions say: \u201cGraph the solution on the number line. Write the solution in interval notation.\u201d To the right of this instruction is a number line ranging from negative 1 to 2, with tick marks at each integer. The inequality is graphed on the number line. Because this is an identity and the solution is all real numbers, the graph is a red line extending in both directions on the number line. Below the number line is the notation: parenthesis, negative infinity comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Simplify each side as much as possible.<\/td>\n<td data-align=\"center\">\\(8x-2\\left(5-x\\right)\\) &lt; \\(4\\left(x+9\\right)+6x\\)<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td data-align=\"center\">\\(8x-10+2x\\) &lt; \\(4x+36+6x\\)<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td data-align=\"center\">\\(10x-10\\) &lt; \\(10x+36\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(10x\\) from both sides to collect the variables on the left.<\/td>\n<td data-align=\"center\">\\(10x-10-10x\\) &lt; \\(10x+36-10x\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"center\">\\(-10\\) &lt; \\(36\\phantom{\\rule{0.6em}{0ex}}\\)<\/td>\n<\/tr>\n<tr>\n<td>The \\(x\\)\u2019s are gone, and we have a true statement.<\/td>\n<td data-align=\"center\">The inequality is an identity.<span data-type=\"newline\">\n<\/span>The solution is all real numbers.<\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461228510\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_049a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td data-align=\"center\">\\(\\left(-\\infty ,\\infty \\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342167586\" data-type=\"problem\">\n<p id=\"fs-id1168345442902\">Solve the inequality \\(4b-3\\left(3-b\\right)\\) &gt; \\(5\\left(b-6\\right)+2b\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345397967\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168341963297\" data-type=\"media\" data-alt=\"This figure shows an inequality that is an identity. Below this inequality is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. The inequality is also written in interval notation as parenthesis, negative infinity comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_050_img_new.jpg\" alt=\"This figure shows an inequality that is an identity. Below this inequality is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. The inequality is also written in interval notation as parenthesis, negative infinity comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341975166\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341975169\" data-type=\"exercise\">\n<div id=\"fs-id1168345695450\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341959544\" data-type=\"problem\">\n<p id=\"fs-id1168341959546\">Solve the inequality \\(\\frac{1}{3}a-\\frac{1}{8}a\\) &gt; \\(\\frac{5}{24}a+\\frac{3}{4}\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345423625\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463871077\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality one-third a minus one-eighth a is greater than five-twenty-fourths a plus 3\/4. One line down to the left, the instructions say: \u201cMultiply both sides by the LCD, 24, to clear the fractions.\u201d To the right of this instruction is the inequality multiplied by 24 on both sides: 24 times one-third a minus one-eighth a, with one-third a minus one-eighth a in parentheses, is greater than 24 times five-twenty-fourths a plus \u00be, with five-twenty-fourths a plus \u00be in parentheses, and \u201c24 times\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the inequality 8a minus 3a is greater than 5a plus 18. Another line down to the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 5a is greater than 5a plus 18. Another line down on the left, the instructions say: \u201cSubtract 5a from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 5a subtracted from both sides: 5a minus 5a is greater than 5a minus 5a plus 18. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality 0 is greater than 18. Another line down on the left, the instructions say: \u201cThe statement is false!\u201d To the right is the text: \u201cThe inequality is a contradiction.\u201d Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this instruction is a number line ranging from negative 1 to 2, with tick marks at each integer. No inequality is graphed on the number line. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this sentence is the text: \u201cThere is no solution.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168459278426\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD, 24, to clear the fractions.<\/td>\n<td><span id=\"eip-id1168459278443\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461145691\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168461804210\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(5a\\) from both sides to collect the variables on the left.<\/td>\n<td><span id=\"eip-id1168461804234\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"fs-id1169147708868\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The statement is false!<\/td>\n<td>The inequality is a contradiction.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>There is no solution.<\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461201953\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td>There is no solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345251538\" data-type=\"problem\">\n<p id=\"fs-id1168345329045\">Solve the inequality \\(\\frac{1}{4}x-\\frac{1}{12}x\\) &gt; \\(\\frac{1}{6}x+\\frac{7}{8}\\), graph the solution on the number line, and write the solution in interval notation.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345217894\" data-type=\"solution\"><details><summary>Show answer<\/summary><span id=\"fs-id1168345647699\" data-type=\"media\" data-alt=\"This figure shows an inequality that is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. No inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution.\u201d\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_053_img_new.jpg\" alt=\"This figure shows an inequality that is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. No inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345500407\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Translate to an Inequality and Solve<\/h1>\n<p id=\"fs-id1168345253149\">To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. Some words are easy, like \u2018more than\u2019 and \u2018less than\u2019. But others are not as obvious.<\/p>\n<p id=\"fs-id1168342101872\">Think about the phrase \u2018at least\u2019 \u2013 what does it mean to be \u2018at least 21 years old\u2019? It means 21 or more. The phrase \u2018at least\u2019 is the same as \u2018greater than or equal to\u2019.<\/p>\n<p id=\"fs-id1168345423772\"><a class=\"autogenerated-content\" href=\"#fs-id1168345688476\">(Figure)<\/a> shows some common phrases that indicate inequalities.<\/p>\n\n<table id=\"fs-id1168345688476\" class=\"grid\" summary=\"This figure is a table with four columns and five rows. The first row, which is a header row, contains inequality symbols. Starting from the first cell to the left, the symbols left to right are: the symbols are is greater than, is greater than or equal to, is less than, and is less than or equal to. Below the header row in the first column are words or phrases that indicate the symbol is greater than. Starting from the second row and going down, these words and phrases are: \u201cis greater than,\u201d \u201cis more than,\u201d \u201cis larger than,\u201d and \u201cexceeds.\u201d Below the header row in the second column are phrases that indicate the symbol is greater than or equal to. Starting from the second row and going down, these phrases are: \u201cgreater than or equal to,\u201d \u201cis at least,\u201d \u201cis no less than,\u201d and \u201cis the minimum.\u201d Below the header row in the third column are phrases that indicate the symbol is less than. Starting from the second row and going down, these phrases are: \u201cis less than,\u201d \u201cis smaller than,\u201d \u201chas fewer than,\u201d and \u201cis lower than.\u201d Below the header row in the last column are phrases that indicate the symbol is less than or equal to. Starting from the second row and going down, these phrases are: \u201cis less than or equal to,\u201d \u201cis at most,\u201d \u201cis no more than,\u201d and \u201cis the maximum.\u201d\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"middle\" data-align=\"center\">&gt;<\/th>\n<th data-valign=\"middle\" data-align=\"center\">\\(\\ge \\)<\/th>\n<th data-valign=\"middle\" data-align=\"center\">&lt;<\/th>\n<th data-valign=\"middle\" data-align=\"center\">\\(\\le \\)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is greater than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is greater than or equal to<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is less than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is less than or equal to<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is more than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is at least<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is smaller than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is at most<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is larger than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is no less than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">has fewer than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is no more than<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">exceeds<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is the minimum<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is lower than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is the maximum<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345720316\" data-type=\"problem\">\n<p id=\"fs-id1168345251022\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169751872347\">Twelve times <em data-effect=\"italics\">c<\/em> is no more than 96.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345416357\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463007039\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the math phrase \u201cTwelve times c is no more than 96, with \u201cis no more than\u201d highlighted with a bracket. One line down to the left, the instructions say: \u201cTranslate.\u201d To the right of this instruction is the inequality 12c is less than or equal to 96. One more line down on the left, the instructions say: \u201cSolve\u2014divide both sides by 12.\u201d To the right of this sentence is the same inequality divided by 12 on both sides: 12c over 12 is less than or equal to 96 over 12. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality c is less than or equal to 8. Another line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the inequality in interval notation: parenthesis, negative infinity comma 8. One more line down on the left, the instructions say: \u201cGraph on the number line.\u201d To the right of this sentence a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is less than or equal to 8 is graphed on the number line, with an open bracket at c equals 8, and a dark line extending from the parenthesis to the left.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td colspan=\"0\"><span id=\"eip-id1168463007056\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve\u2014divide both sides by 12.<\/td>\n<td><span id=\"eip-id1168463007073\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463007090\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463007108\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph on the number line.<\/td>\n<td><span id=\"eip-id1168463007125\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345424285\" data-type=\"problem\">\n<p id=\"fs-id1168345424288\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1168342156018\">Twenty times <em data-effect=\"italics\">y<\/em> is at most 100<\/p>\n\n<\/div>\n<div id=\"fs-id1168345425365\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary><span id=\"fs-id1168345425368\" data-type=\"media\" data-alt=\"This figure shows the inequality 20y is less than or equal to 100, and then its solution: y is less than or equal to 5. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality y is less than or equal to 5 is graphed on the number line, with an open bracket at y equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_056_img_new.jpg\" alt=\"This figure shows the inequality 20y is less than or equal to 100, and then its solution: y is less than or equal to 5. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality y is less than or equal to 5 is graphed on the number line, with an open bracket at y equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342079179\" data-type=\"problem\">\n<p id=\"fs-id1168342079181\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169751893803\">Thirty less than <em data-effect=\"italics\">x<\/em> is at least 45.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345743107\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463004929\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the math phrase \u201cThirty less than x is at least 45, with \u201cis at least\u201d highlighted with a bracket. One line down to the left, the instructions say: \u201cTranslate.\u201d To the right of this instruction is the inequality x minus 30 is greater than or equal to 45. One more line down on the left, the instructions say: \u201cSolve\u2014add 30 to both sides.\u201d To the right of this sentence is the same inequality with 30 added to both sides: x minus 30 plus 30 is greater than or equal to 45 plus 30, with \u201cplus 30\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality x is greater than or equal to 75. Another line down to the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this instruction is the inequality in interval notation: bracket, 75 comma infinity, parenthesis. One more line down on the left, the instructions say: \u201cGraph on the number line.\u201d To the right of this sentence is a number line ranging from 74 to 77 with tick marks for each integer. The inequality x is greater than or equal to 75 is graphed on the number line, with an open bracket at x equals 75, and a red line extending to the right of the bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168463004966\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve\u2014add 30 to both sides.<\/td>\n<td><span id=\"eip-id1168463004983\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463005000\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463005017\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph on the number line.<\/td>\n<td><span id=\"eip-id1168463005035\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345530275\" data-type=\"problem\">\n<p id=\"fs-id1168345259208\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169754028949\">Nineteen less than <em data-effect=\"italics\">p<\/em> is no less than 47<\/p>\n\n<\/div>\n<div id=\"fs-id1168345196869\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary><span id=\"fs-id1168345407099\" data-type=\"media\" data-alt=\"This figure shows the inequality p minus 19 is greater than or equal to 47, and then its solution: p is greater than or equal to 66. Below this inequality is a number line ranging from 65 to 69 with tick marks for each integer. The inequality p is greater than or equal to 66 is graphed on the number line, with an open bracket at p equals 66, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 66 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_059_img_new.jpg\" alt=\"This figure shows the inequality p minus 19 is greater than or equal to 47, and then its solution: p is greater than or equal to 66. Below this inequality is a number line ranging from 65 to 69 with tick marks for each integer. The inequality p is greater than or equal to 66 is graphed on the number line, with an open bracket at p equals 66, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 66 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul>\n \t<li><strong data-effect=\"bold\">Subtraction Property of Inequality<\/strong><span data-type=\"newline\">\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\">\n<\/span> if \\(a\\) &lt; \\(b\\) then \\(a-c\\) &lt; \\(b-c\\) and<span data-type=\"newline\">\n<\/span> if \\(a\\) &gt; \\(b\\) then \\(a-c\\) &gt; \\(b-c.\\)<\/li>\n \t<li><strong data-effect=\"bold\">Addition Property of Inequality<\/strong><span data-type=\"newline\">\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\">\n<\/span> if \\(a\\) &lt; \\(b\\) then \\(a+c\\) &lt; \\(b+c\\) and<span data-type=\"newline\">\n<\/span> if \\(a\\) &gt; \\(b\\) then \\(a+c\\) &gt; \\(b+c.\\)<\/li>\n \t<li><strong data-effect=\"bold\">Division and Multiplication Properties of Inequalit<\/strong><strong data-effect=\"bold\">y<\/strong><span data-type=\"newline\">\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\">\n<\/span> if \\(a\\) &lt; \\(b\\) and \\(c\\) &gt; \\(0\\), then \\(\\frac{a}{c}\\) &lt; \\(\\frac{b}{c}\\) and \\(ac\\) &gt; \\(bc\\).<span data-type=\"newline\">\n<\/span> if \\(a\\) &gt; \\(b\\) and \\(c\\) &gt; \\(0\\), then \\(\\frac{a}{c}\\) &gt; \\(\\frac{b}{c}\\) and \\(ac\\) &gt; \\(bc\\).<span data-type=\"newline\">\n<\/span> if \\(a\\) &lt; \\(b\\) and \\(c\\) &lt; \\(0\\), then \\(\\frac{a}{c}\\) &gt; \\(\\frac{b}{c}\\) and \\(ac\\) &gt; \\(bc\\).<span data-type=\"newline\">\n<\/span> if \\(a\\) &gt; \\(b\\) and \\(c\\) &lt; \\(0\\), then \\(\\frac{a}{c}\\) &lt; \\(\\frac{b}{c}\\) and \\(ac\\) &lt; \\(bc\\).<span data-type=\"newline\">\n<\/span><\/li>\n \t<li>When we <strong data-effect=\"bold\">divide or multiply<\/strong> an inequality by a:\n<ul id=\"fs-id1168345543646\" data-bullet-style=\"open-circle\">\n \t<li><strong data-effect=\"bold\">positive<\/strong> number, the inequality stays the <strong data-effect=\"bold\">same<\/strong>.<\/li>\n \t<li><strong data-effect=\"bold\">negative<\/strong> number, the inequality <strong data-effect=\"bold\">reverses<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>2.5 Exercise Set<\/h1>\n<p id=\"fs-id1169749983130\">In the following exercises, graph each inequality on the number line.<\/p>\n\n<ol class=\"twocolumn\">\n \t<li>\n<ol type=\"a\">\n \t<li>\\(x\\) &gt; \\(1\\)<\/li>\n \t<li>\\(x\\) &lt; \\(-2\\)<\/li>\n \t<li>\\(x \\ge -3\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\n<ol type=\"a\">\n \t<li>\\(x\\le 0\\)<\/li>\n \t<li>\\(x\\) &gt; \\(-4\\)<\/li>\n \t<li>\\(x\\ge -1\\)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1168345450007\">In the following exercises, graph each inequality on the number line and write in interval notation.<\/p>\n\n<ol class=\"twocolumn\" start=\"3\">\n \t<li>\n<ol type=\"a\">\n \t<li>\\(x\\) &gt; \\(3\\)<\/li>\n \t<li>\\(x\\le -0.5\\)<\/li>\n \t<li>\\(x\\ge \\frac{1}{3}\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\n<ol type=\"a\">\n \t<li>\\(x\\le 5\\)<\/li>\n \t<li>\\(x\\ge -1.5\\)<\/li>\n \t<li>\\(x\\) &lt; \\(-\\frac{7}{3}\\)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div id=\"fs-id1168345442027\" data-type=\"exercise\">\n<div id=\"fs-id1168345442029\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<\/div>\n<div id=\"fs-id1168345454367\" data-type=\"exercise\">\n<div id=\"fs-id1168345454369\" data-type=\"problem\">\n<ol class=\"twocolumn\" start=\"5\">\n \t<li>\\(m-45\\le 62\\)<\/li>\n \t<li>\\(v+12\\) &gt; \\(3\\)<\/li>\n \t<li>\\(b+\\frac{7}{8}\\ge \\frac{1}{6}\\)<\/li>\n \t<li>\\(g-\\frac{11}{12}\\) &lt; \\(-\\frac{5}{18}\\)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341861931\" data-type=\"exercise\">\n<div id=\"fs-id1168341861933\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"9\">\n \t<li>\\(6y\\) &lt; \\(48\\)<\/li>\n \t<li>\\(9s\\ge 81\\)<\/li>\n \t<li>\\(-8v\\le 96\\)<\/li>\n \t<li>\\(-7d\\) &gt; \\(105\\)<\/li>\n \t<li>\\(40\\) &lt; \\(\\frac{5}{8}k\\)<\/li>\n \t<li>\\(\\frac{9}{4}g\\le 36\\)<\/li>\n \t<li>\\(\\frac{b}{-10}\\ge 30\\)<\/li>\n \t<li>\\(-18\\) &gt; \\(\\frac{q}{-6}\\)<\/li>\n \t<li>\\(7s\\) &lt; \\(-28\\)<\/li>\n \t<li>\\(\\frac{3}{5}x\\le -45\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345543040\" data-type=\"exercise\">\n<div id=\"fs-id1168345543042\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<\/div>\n<div id=\"fs-id1168345449792\" data-type=\"exercise\">\n<div id=\"fs-id1168345449795\" data-type=\"problem\">\n<ol class=\"twocolumn\" start=\"19\">\n \t<li>\\(5u\\le 8u-21\\)<\/li>\n \t<li>\\(9p\\) &gt; \\(14p+18\\)<\/li>\n \t<li>\\(9y+5\\left(y+3\\right)\\) &lt; \\(4y-35\\)<\/li>\n \t<li>\\(4k-\\left(k-2\\right)\\ge 7k-26\\)<\/li>\n \t<li>\\(6n-12\\left(3-n\\right)\\le 9\\left(n-4\\right)+9n\\)<\/li>\n \t<li>\\(9u+5\\left(2u-5\\right)\\ge 12\\left(u-1\\right)+7u\\)<\/li>\n \t<li>\\(\\frac{5}{6}a-\\frac{1}{4}a\\) &gt; \\(\\frac{7}{12}a+\\frac{2}{3}\\)<\/li>\n \t<li>\\(12v+3\\left(4v-1\\right)\\le 19\\left(v-2\\right)+5v\\)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345726340\" data-type=\"exercise\">\n<div id=\"fs-id1168345726342\" data-type=\"problem\"><span style=\"orphans: 1; text-align: initial; font-size: 14pt;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"27\">\n \t<li>\\(35k\\ge -77\\)<\/li>\n \t<li>\\(18q-4\\left(10-3q\\right)\\) &lt; \\(5\\left(6q-8\\right)\\)<\/li>\n \t<li>\\(-\\frac{21}{8}y\\le -\\frac{15}{28}\\)<\/li>\n \t<li>\\(d+29\\) &gt; \\(-61\\)<\/li>\n \t<li>\\(\\frac{n}{13}\\le -6\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345511366\" data-type=\"exercise\">\n<div id=\"fs-id1168345511368\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"32\">\n \t<li>Ninety times <em data-effect=\"italics\">c<\/em> is less than 450.<\/li>\n \t<li>Ten times <em data-effect=\"italics\">y<\/em> is at most \\(-110\\).<\/li>\n \t<li>Six more than <em data-effect=\"italics\">k<\/em> exceeds 25.<\/li>\n \t<li>Twelve less than <em data-effect=\"italics\">x<\/em> is no less than 21.<\/li>\n \t<li>Negative two times <em data-effect=\"italics\">s<\/em> is lower than 56.<\/li>\n \t<li>Fifteen less than <em data-effect=\"italics\">a<\/em> is at least \\(-7\\).<\/li>\n \t<li>The maximum height, <em data-effect=\"italics\">h<\/em>, of a fighter pilot is 77 inches. Write this as an inequality.<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345287059\" data-type=\"exercise\">\n<h1>Answers<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 1633px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 329px;\">\n<td style=\"width: 33.3333%; height: 329px;\"><span class=\"token\">1. <\/span>\n\n<span class=\"token\">a.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345408756\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 1 is graphed on the number line, with an open parenthesis at x equals 1, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_204_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 1 is graphed on the number line, with an open parenthesis at x equals 1, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">b.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168341854168\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the left of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_205_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">c.<\/span><span id=\"fs-id1168345255064\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 3 is graphed on the number line, with an open bracket at x equals negative 3, and a dark line extending to the right of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_206_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 3 is graphed on the number line, with an open bracket at x equals negative 3, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 329px;\">2.\n\n<span class=\"token\">a.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345415049\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 0 is graphed on the number line, with an open bracket at x equals 0, and a dark line extending to the left of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_210_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 0 is graphed on the number line, with an open bracket at x equals 0, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">b.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345650393\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 4 is graphed on the number line, with an open parenthesis at x equals negative 4, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_211_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 4 is graphed on the number line, with an open parenthesis at x equals negative 4, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span data-type=\"newline\">c.\n<\/span><span id=\"fs-id1168345538820\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_212_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 329px;\">3.\n\n<span class=\"token\">a.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345650400\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the right of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, 3 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_216_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the right of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, 3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">b.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345431173\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 0.5 is graphed on the number line, with an open bracket at x equals negative 0.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 0.5, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_217_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 0.5 is graphed on the number line, with an open bracket at x equals negative 0.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 0.5, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">c.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345443821\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1\/3 is graphed on the number line, with an open bracket at x equals 1\/3 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 1\/3 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_218_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1\/3 is graphed on the number line, with an open bracket at x equals 1\/3 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 1\/3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 361px;\">\n<td style=\"width: 33.3333%; height: 361px;\">4.\n\n<span class=\"token\">a.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168342181524\" data-type=\"media\" data-alt=\"This figure is a number line with tick marks. The inequality x is less than or equal to 5 is graphed on the number line, with an open bracket at x equals 5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 5, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_222_img_new.jpg\" alt=\"This figure is a number line with tick marks. The inequality x is less than or equal to 5 is graphed on the number line, with an open bracket at x equals 5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 5, bracket.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">b.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345695399\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 1.5 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_223_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 1.5 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">c.<\/span><span data-type=\"newline\">\n<\/span><span id=\"fs-id1168345538809\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 7\/3 is graphed on the number line, with an open parenthesis at x equals negative 7\/3 (written in), and a dark line extending to the left of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 7\/3, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_224_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 7\/3 is graphed on the number line, with an open parenthesis at x equals negative 7\/3 (written in), and a dark line extending to the left of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 7\/3, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 361px;\">5. <span id=\"fs-id1168341955831\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_226_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 361px;\">6. <span id=\"fs-id1168345292799\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_228_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 125px;\">\n<td style=\"width: 33.3333%; height: 125px;\">7. <span id=\"fs-id1168345398216\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17\/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17\/24 is graphed on the number line, with an open bracket at b equals negative 17\/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17\/24 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_230_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17\/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17\/24 is graphed on the number line, with an open bracket at b equals negative 17\/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17\/24 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 125px;\">8. <span id=\"fs-id1168345386567\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: g is less than 23\/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23\/26 is graphed on the number line, with an open parenthesis at g equals 23\/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23\/26, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_232_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: g is less than 23\/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23\/26 is graphed on the number line, with an open parenthesis at g equals 23\/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23\/26, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 125px;\">9. <span data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_234_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 96px;\">\n<td style=\"width: 33.3333%; height: 96px;\">10. <span id=\"fs-id1168345326014\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_236_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 96px;\">11. <span id=\"fs-id1168341955773\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_238_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 96px;\">12. <span id=\"fs-id1168341857412\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_240_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 95px;\">\n<td style=\"width: 33.3333%; height: 95px;\">13. <span id=\"fs-id1168345560404\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_243_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">14. <span id=\"fs-id1168345261323\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_245_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">15. <span id=\"fs-id1168345284656\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_247_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 95px;\">\n<td style=\"width: 33.3333%; height: 95px;\">16. <span id=\"fs-id1168345543291\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_249_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">17. <span id=\"fs-id1168345551424\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_251_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">18. <span id=\"fs-id1168345346824\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_253_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 119px;\">\n<td style=\"width: 33.3333%; height: 119px;\">19. <span id=\"fs-id1168345426423\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_255_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 119px;\">20. <span id=\"fs-id1168345637187\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: p is less than 18\/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18\/5 is graphed on the number line, with an open parenthesis at p equals 18\/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18\/5, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_257_img.jpg\" alt=\"At the top of this figure is the solution to the inequality: p is less than 18\/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18\/5 is graphed on the number line, with an open parenthesis at p equals 18\/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18\/5, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 119px;\">21. <span id=\"fs-id1168345448056\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_259_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">22. <span id=\"fs-id1168345432888\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_261_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. <span id=\"fs-id1168345409518\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_263_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">24. <span id=\"fs-id1168345529489\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_265_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. <span id=\"fs-id1168345388259\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_267_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">26. <span id=\"fs-id1168345549932\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_269_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. <span id=\"fs-id1168345250280\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11\/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11\/5 is graphed on the number line, with an open bracket at k equals negative 11\/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11\/5 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_271_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11\/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11\/5 is graphed on the number line, with an open bracket at k equals negative 11\/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11\/5 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 101px;\">\n<td style=\"width: 33.3333%; height: 101px;\">28. <span id=\"fs-id1168345576994\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_273_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 101px;\">29. <span id=\"fs-id1168345500573\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is greater than or equal to 10\/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10\/49 is graphed on the number line, with an open bracket at y equals 10\/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10\/49 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_275_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is greater than or equal to 10\/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10\/49 is graphed on the number line, with an open bracket at y equals 10\/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10\/49 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 101px;\">30. <span id=\"fs-id1168345640013\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_277_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 94px;\">\n<td style=\"width: 33.3333%; height: 94px;\">31. <span id=\"fs-id1168345675913\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_279_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 94px;\">32. <span id=\"fs-id1168345550085\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_281_img_new.jpg\" alt=\"At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 94px;\">33. <span id=\"fs-id1168345540607\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_283_img_new.jpg\" alt=\"At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 93px;\">\n<td style=\"width: 33.3333%; height: 93px;\">34. <span id=\"fs-id1168345708306\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_285_img_new.jpg\" alt=\"At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">35. <span id=\"fs-id1168345633327\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_287_img_new.jpg\" alt=\"At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">36. <span id=\"fs-id1168345742297\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_289_img_new.jpg\" alt=\"At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 93px;\">\n<td style=\"width: 33.3333%; height: 93px;\">37. <span id=\"fs-id1168345569269\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_291_img_new.jpg\" alt=\"At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">38. \\(h\\le 77\\)<\/td>\n<td style=\"width: 33.3333%; height: 93px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n&nbsp;","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Graph inequalities on the number line<\/li>\n<li>Solve inequalities using the Subtraction and Addition Properties of inequality<\/li>\n<li>Solve inequalities using the Division and Multiplication Properties of inequality<\/li>\n<li>Solve inequalities that require simplification<\/li>\n<li>Translate to an inequality and solve<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Graph Inequalities on the Number Line<\/h1>\n<div id=\"fs-id1168345725112\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1168345197716\">Do you remember what it means for a number to be a solution to an equation? A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/p>\n<p id=\"fs-id1168345465826\">What about the solution of an inequality? What number would make the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> true? Are you thinking, \u2018<em data-effect=\"italics\">x<\/em> could be 4\u2019? That\u2019s correct, but <em data-effect=\"italics\">x<\/em> could be 5 too, or 20, or even 3.001. Any number greater than 3 is a solution to the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1168345507984\">We show the solutions to the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> on the number line by shading in all the numbers to the right of 3, to show that all numbers greater than 3 are solutions. Because the number 3 itself is not a solution, we put an open parenthesis at 3. The graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_001\">(Figure)<\/a>. Please note that the following convention is used: light blue arrows point in the positive direction and dark blue arrows point in the negative direction.<\/p>\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is graphed on this number line.<\/div>\n<p><span id=\"fs-id1168345484183\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_02_07_001_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1168341909119\">The graph of the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-120e3ca4a174b2b6e2d82155e17c0d45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\" \/> is very much like the graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, but now we need to show that 3 is a solution, too. We do that by putting a bracket at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_002_img_new\">(Figure)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_002_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-120e3ca4a174b2b6e2d82155e17c0d45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\" \/> is graphed on this number line.<\/div>\n<p><span id=\"fs-id1168345414614\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3 is graphed on the number line, with an open bracket at x equals 3, and a red line extending to the right of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_002_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3 is graphed on the number line, with an open bracket at x equals 3, and a red line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1168345255661\">Notice that the open parentheses symbol, (, shows that the endpoint of the inequality is not included. The open bracket symbol, [, shows that the endpoint is included.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345512685\" data-type=\"problem\">\n<p id=\"fs-id1168345744388\">Graph on the number line:<\/p>\n<p id=\"fs-id1168345273771\"><span class=\"token\">a) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-34c375dd6b737c15ca9401bc0e9e9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1168345723696\" data-type=\"solution\">\n<p style=\"padding-left: 40px;\"><span class=\"token\">a) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-34c375dd6b737c15ca9401bc0e9e9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\" \/><span data-type=\"newline\"><br \/>\n<\/span> This means all numbers less than or equal to 1. We shade in all the numbers on the number line to the left of 1 and put a bracket at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/> to show that it is included.<span data-type=\"newline\"><br \/>\n<\/span> <span id=\"fs-id1168345274106\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_003_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">b) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><span data-type=\"newline\"><br \/>\n<\/span> This means all numbers less than 5, but not including 5. We shade in all the numbers on the number line to the left of 5 and put a parenthesis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> to show it is not included.<span data-type=\"newline\"><br \/>\n<\/span> <span id=\"fs-id1168345408217\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 5 is graphed on the number line, with an open parenthesis at x equals 5, and a red line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_004_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 5 is graphed on the number line, with an open parenthesis at x equals 5, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">c) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><span data-type=\"newline\"><br \/>\n<\/span> This means all numbers greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>, but not including <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>. We shade in all the numbers on the number line to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>, then put a parenthesis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/> to show it is not included.<span data-type=\"newline\"><br \/>\n<\/span> <span id=\"fs-id1168345452718\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 1 is graphed on the number line, with an open parenthesis at x equals negative 1, and a red line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_005_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 1 is graphed on the number line, with an open parenthesis at x equals negative 1, and a red line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345443645\" data-type=\"problem\">\n<p id=\"fs-id1168345557090\">Graph on the number line: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71173cb3520cc7f6bc259c3176f8a66a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt;\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345434561\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">a)<br \/>\n<\/span><span data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the left of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_006_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">b)<br \/>\n<\/span><span id=\"fs-id1168345622953\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_007_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-type=\"newline\">c)<br \/>\n<\/span><span id=\"fs-id1168345687655\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the left of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_008_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345250830\">We can also represent inequalities using <em data-effect=\"italics\">interval notation.<\/em> As we saw above, the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> means all numbers greater than 3. There is no upper end to the solution to this inequality. In <span class=\"no-emphasis\" data-type=\"term\">interval notation<\/span>, we express <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa6bc95909d9315ebcae3a094b0e1e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -4px;\" \/> The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-93c44e61f4f297faa7e306b7ae24b62d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"16\" style=\"vertical-align: 0px;\" \/> is read as \u2018infinity\u2019. It is not an actual number. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_012_img_new\">(Figure)<\/a> shows both the number line and the interval notation.<\/p>\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_012_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is graphed on this number line and written in interval notation.<\/div>\n<p><span data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 3 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_012_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1168345456146\">The inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-34c375dd6b737c15ca9401bc0e9e9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\" \/> means all numbers less than or equal to 1. There is no lower end to those numbers. We write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-34c375dd6b737c15ca9401bc0e9e9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\" \/> in interval notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-337adbf4f3220a1b09001f19e88045a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/>. The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-46ff86acf9d540b0b8101bd9737e8e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"30\" style=\"vertical-align: 0px;\" \/> is read as \u2018negative infinity\u2019. <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_013_img_new\">(Figure)<\/a> shows both the number line and interval notation.<\/p>\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_013_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-34c375dd6b737c15ca9401bc0e9e9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\" \/> is graphed on this number line and written in interval notation.<\/div>\n<p><span id=\"fs-id1168345241928\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 1, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_013_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 1, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"note\">\n<div data-type=\"title\">Inequalities, Number Lines, and Interval Notation<\/div>\n<p><span id=\"fs-id1168345291600\" data-type=\"media\" data-alt=\"This figure show four number lines, all without tick marks. The inequality x is greater than a is graphed on the first number line, with an open parenthesis at x equals a, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, a comma infinity, parenthesis. The inequality x is greater than or equal to a is graphed on the second number line, with an open bracket at x equals a, and a red line extending to the right of the bracket. The inequality is also written in interval notation as bracket, a comma infinity, parenthesis. The inequality x is less than a is graphed on the third number line, with an open parenthesis at x equals a, and a red line extending to the left of the parenthesis. The inequality is also written in interval notation as parenthesis, negative infinity comma a, parenthesis. The inequality x is less than or equal to a is graphed on the last number line, with an open bracket at x equals a, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma a, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_014_img_new.jpg\" alt=\"This figure show four number lines, all without tick marks. The inequality x is greater than a is graphed on the first number line, with an open parenthesis at x equals a, and a red line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, a comma infinity, parenthesis. The inequality x is greater than or equal to a is graphed on the second number line, with an open bracket at x equals a, and a red line extending to the right of the bracket. The inequality is also written in interval notation as bracket, a comma infinity, parenthesis. The inequality x is less than a is graphed on the third number line, with an open parenthesis at x equals a, and a red line extending to the left of the parenthesis. The inequality is also written in interval notation as parenthesis, negative infinity comma a, parenthesis. The inequality x is less than or equal to a is graphed on the last number line, with an open bracket at x equals a, and a red line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma a, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p>Did you notice how the parenthesis or bracket in the interval notation matches the symbol at the endpoint of the arrow? These relationships are shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Ch02_Figure_02_07_015_img_new\">(Figure)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Ch02_Figure_02_07_015_img_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The notation for inequalities on a number line and in interval notation use similar symbols to express the endpoints of intervals.<\/div>\n<p><span id=\"fs-id1168345623160\" data-type=\"media\" data-alt=\"This figure shows the same four number lines as above, with the same interval notation labels. Below the interval notation for each number line, there is text indicating how the notation on the number lines is similar to the interval notation. The first number line is a graph of x is greater than a, and the interval notation is parenthesis, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left parenthesis.\u201d The second number line is a graph of x is greater than or equal to a, and the interval notation is bracket, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left bracket.\u201d The third number line is a graph of x is less than a, and the interval notation is parenthesis, negative infinity comma a, parenthesis. The text below reads: \u201cBoth have a right parenthesis.\u201d The last number line is a graph of x is less than or equal to a, and the interval notation is parenthesis, negative infinity comma a, bracket. The text below reads: \u201cBoth have a right bracket.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_015_img_new.jpg\" alt=\"This figure shows the same four number lines as above, with the same interval notation labels. Below the interval notation for each number line, there is text indicating how the notation on the number lines is similar to the interval notation. The first number line is a graph of x is greater than a, and the interval notation is parenthesis, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left parenthesis.\u201d The second number line is a graph of x is greater than or equal to a, and the interval notation is bracket, a comma infinity, parenthesis. The text below reads: \u201cBoth have a left bracket.\u201d The third number line is a graph of x is less than a, and the interval notation is parenthesis, negative infinity comma a, parenthesis. The text below reads: \u201cBoth have a right parenthesis.\u201d The last number line is a graph of x is less than or equal to a, and the interval notation is parenthesis, negative infinity comma a, bracket. The text below reads: \u201cBoth have a right bracket.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345239191\" data-type=\"problem\">\n<p id=\"fs-id1168341847896\">Graph on the number line and write in interval notation.<\/p>\n<p id=\"fs-id1168345550454\"><span class=\"token\">a) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dfc84780b14328431bcc372ff904772d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -3px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-76a0bbe2b3a9634ad0904e6d7b6c8813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345453189\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span class=\"token\">a)<\/span><span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"eip-id1168465214382\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is greater than or equal to negative 3. One line down on the left, the instructions say: \u201cShade to the right of negative 3, and put a bracket at negative 3.\u201d To the right of this sentence is a number line ranging from negative 4 to negative 1, with tick marks at each integer. There is a bracket at negative 3 and a red line extends to the right from negative 3. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: bracket, negative 3 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465214399\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>, and put a bracket at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168465214426\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168465214443\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span data-type=\"newline\">b)<\/span><\/p>\n<table id=\"eip-id1168463870324\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is less than 2.5. One line down on the left, the instructions say: \u201cShade to the left of 2.5, and put a parenthesis at 2.5.\u201d To the right of this sentence is a number line ranging from 0 to 3, with tick marks at each integer. There is a parenthesis at 2.5 (written in) and a red line extends to the left from 2.5. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: parenthesis, negative infinity comma 2.5, parethesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463870342\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>, and put a parenthesis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168463870368\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463870385\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_017c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span data-type=\"newline\">c)<\/span><\/p>\n<table id=\"eip-id1168465191280\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left, and math on the right. At the top of the figure on the right is the inequality x is less than or equal to negative 3\/5. One line down on the left, the instructions say: \u201cShade to the left of negative 3\/5, and put a bracket at negative 3\/5.\u201d To the right of this sentence is a number line ranging from negative 2 to 1, with tick marks at each integer. There is a bracket at negative 3\/5 (written in) and a red line extends to the left from negative 3\/5. Another line down on the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this sentence is the interval notation: parenthesis, negative infinity comma negative three fifths, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465191297\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Shade to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cfb86af023a3aff3c54b9ecc49551a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/>, and put a bracket at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cfb86af023a3aff3c54b9ecc49551a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><span id=\"eip-id1168465191334\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168465191352\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345420817\" data-type=\"problem\">\n<p id=\"fs-id1168345407937\">Graph on the number line and write in interval notation:<\/p>\n<p id=\"fs-id1168345297606\"><span class=\"token\">a) <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0a9adac4c3934e690a9c3e3eceb7215c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#45;&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"70\" style=\"vertical-align: -3px;\" \/>c)\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b2488cb98c75d364cc8619ebc435fa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345291328\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p style=\"padding-left: 40px;\"><span class=\"token\">a)<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345448172\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 2 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_019_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 2 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">b)<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345579989\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 1.5, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_020_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 1.5, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"padding-left: 40px;\"><span class=\"token\">c)<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345435633\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3\/4 is graphed on the number line, with an open bracket at x equals 3\/4, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 3\/4 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_021_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3\/4 is graphed on the number line, with an open bracket at x equals 3\/4, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 3\/4 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345517735\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Solve Inequalities using the Subtraction and Addition Properties of Inequality<\/h1>\n<p id=\"fs-id1168345293507\">The Subtraction and Addition Properties of Equality state that if two quantities are equal, when we add or subtract the same amount from both quantities, the results will be equal.<\/p>\n<div id=\"fs-id1168345241070\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a86da32231723c60ed5e077bb8b776a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#100;&#100;&#105;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#45;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#45;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#43;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"540\" style=\"vertical-align: -35px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345630854\">Similar properties hold true for inequalities.<\/p>\n<table id=\"eip-id1168461203088\" class=\"unnumbered unstyled can-break\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cFor example, we know that negative 4 is less than 2.\u201d To the right of this instruction is the inequality negative 4 is less than 2. One line down on the left, the instructions say: \u201cIf we subtract 5 from both quantities, is the left side still less than the right side?\u201d To the right of this instruction is the original inequality with 5 subtracted from both sides: negative 4 minus 5 question mark 2 minus 5. Another line down on the left, the instructions say: \u201cWe get negative 9 on the left and negative 3 on the right.\u201d To the right of this sentence is the line negative 9 question mark negative 3. Another line down on the left, the instructions say: \u201cAnd we know negative 9 is less then negative 3.\u201d To the right of this sentence is the inequality negative 9 is less than negative 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td>For example, we know that \u22124 is less than 2.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203102\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>If we subtract 5 from both quantities, is the<span data-type=\"newline\"><br \/>\n<\/span>left side still less than the right side?<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203119\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We get \u22129 on the left and \u22123 on the right.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203136\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>And we know \u22129 is less than \u22123.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1168461203154\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_025d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><strong data-effect=\"bold\">The inequality sign stayed the same.<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345216274\">Similarly we could show that the inequality also stays the same for addition.<\/p>\n<p id=\"fs-id1168345408152\">This leads us to the Subtraction and Addition Properties of Inequality.<\/p>\n<div data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Inequality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6410\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.39.52-PM.png\" alt=\"\" width=\"2384\" height=\"722\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345277860\">We use these properties to solve inequalities, taking the same steps we used to solve equations. Solving the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8460de4d864e6fdae466286d2a8b2d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, the steps would look like this:<\/p>\n<table id=\"eip-608\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8460de4d864e6fdae466286d2a8b2d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides to isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22a0f86b90534beb356a53578fdda854_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#53;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"70\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-377135ace5e15424033063c47aeb923f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345742500\">Any number greater than 4 is a solution to this inequality.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345328196\" data-type=\"problem\">\n<p id=\"fs-id1168345215094\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dc91ee62072ce4b58287cd4a51bf760a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"76\" style=\"vertical-align: -6px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345429191\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461308445\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality n minus \u00bd is less than or equal to 5\/8. One line down on the left, the instructions say: \u201cAdd \u00bd to both sides of the inequality.\u201d To the right of this instruction is the same inequality with \u00bd added to both sides: n minus \u00bd plus \u00bd is less than or equal to 5\/8 plus \u00bd. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the inequality n is less than or equal to 9\/8. One more line down on the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from 0 to 3 with n is less than or equal to 9\/8 graphed on it. There is a bracket at n equals 9\/8, and a red line extends to the left from 9\/8. Another line down on the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the interval notation for the graph: parenthesis, negative infinity comma 9\/8, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168461308479\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8fa03e1b526c6d07ec843385490ca4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> to both sides of the inequality.<\/td>\n<td><span id=\"eip-id1168461308504\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461308521\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461308538\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_026d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168461308555\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"CNX_ElemAlg_Figure_02_07_026e_img_new.jpg#fixme#fixme#fixme\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345454848\" data-type=\"problem\">\n<p id=\"fs-id1168345559943\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345429017\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7e870c2527c1621990d9d871eb36853d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#103;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168341901859\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345256519\" data-type=\"media\" data-alt=\"This figure shows the inequality p is greater than or equal to 11\/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at p equals 11\/12, and a dark line extends to the right from 11\/12. Below the number line is the solution written in interval notation: bracket, 11\/12 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_027_img_new.jpg\" alt=\"This figure shows the inequality p is greater than or equal to 11\/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at p equals 11\/12, and a dark line extends to the right from 11\/12. Below the number line is the solution written in interval notation: bracket, 11\/12 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div id=\"fs-id1168345292080\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345644774\" data-type=\"exercise\">\n<div id=\"fs-id1168345454848\" data-type=\"problem\">\u00a0<span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif; font-size: 1.2em; font-weight: bold;\">Solve Inequalities using the Division and Multiplication Properties of Inequality<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345667361\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1168341853058\">The Division and Multiplication Properties of Equality state that if two quantities are equal, when we divide or multiply both quantities by the same amount, the results will also be equal (provided we don\u2019t divide by 0).<\/p>\n<div id=\"fs-id1168345278408\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5ab5a12f54eba1973927eaa98abb9460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#118;&#105;&#115;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#99;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#92;&#110;&#101;&#32;&#48;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#97;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"585\" style=\"vertical-align: -39px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168341857701\">Are there similar properties for inequalities? What happens to an inequality when we divide or multiply both sides by a constant?<\/p>\n<p id=\"fs-id1168345223956\">Consider some numerical examples.<\/p>\n<table id=\"eip-id1168463786734\" summary=\"This figure shows the results of dividing and multiplying an inequality by the same constant. The figure has four columns, with written instructions in the first and third columns, and math in the second and fourth columns. At the top of the figure, the inequality 10 is less than 15 appears at the top of the second and fourth columns. One line down the left, the instructions say: \u201cDivide both sides by 5.\u201d To the right of this sentence is the inequality divided by 5 on both sides: 10 over 5 question mark 15 over 5. To the right of this is the instruction: \u201cMultiply both sides by 5.\u201d To the right of this is the original inequality multiplied by 5 on both sides: 10 times 5 question mark 15 times 5. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the line 2 question mark 3. The third column is blank here. In the fourth column is the line 50 question mark 75. Another line down to the left, the instructions say: \u201cFill in the inequality signs.\u201d To the right of this sentence is the inequality 2 is less than 3. The third column is blank here. In the fourth column is the inequality 50 is less than 75.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463749570\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461145237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 5.<\/td>\n<td><span id=\"eip-id1168461145254\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td>Multiply both sides by 5.<\/td>\n<td><span id=\"eip-id1168461145268\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463992619\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168463992633\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Fill in the inequality signs.<\/td>\n<td><span id=\"eip-id1168463992650\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168464056892\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_029h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1171792354443\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7eac6a14cb396f95ebafb59440865d4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#105;&#110;&#101;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#32;&#115;&#105;&#103;&#110;&#115;&#32;&#115;&#116;&#97;&#121;&#101;&#100;&#32;&#116;&#104;&#101;&#32;&#115;&#97;&#109;&#101;&#46;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"290\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"fs-id1168345389883\">Does the inequality stay the same when we divide or multiply by a negative number?<\/p>\n<table id=\"eip-id1168463765216\" class=\"unnumbered unstyled\" summary=\"This figure shows the results of dividing and multiplying an inequality by the same negative constant. The figure has four columns, with written instructions in the first and third columns, and math in the second and fourth columns. At the top of the figure, the inequality 10 is less than 15 appears at the top of the second and fourth columns. One line down the left, the instructions say: \u201cDivide both sides by negative 5.\u201d To the right of this sentence is the inequality divided by negative 5 on both sides: 10 over negative 5 question mark 15 over negative 5. To the right of this is the instruction: \u201cMultiply both sides by negative 5.\u201d To the right of this is the original inequality multiplied by negative 5 on both sides: 10 times negative 5 question mark 15 times negative 5. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the line negative 2 question mark negative 3. The third column is blank here. In the fourth column is the line negative 50 question mark negative 75. Another line down to the left, the instructions say: \u201cFill in the inequality signs.\u201d To the right of this sentence is the inequality negative 2 is greater than negative 3. The third column is blank here. In the fourth column is the inequality negative 50 is greater than negative 75.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168464590083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461229936\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by \u22125.<\/td>\n<td><span id=\"eip-id1168461229953\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td>Multiply both sides by \u22125.<\/td>\n<td><span id=\"eip-id1168463888075\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463888091\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168461292100\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Fill in the inequality signs.<\/td>\n<td><span id=\"eip-id1168461292116\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><span id=\"eip-id1168463779381\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_030h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1171792498411\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-857bd36a42e6e9e65b49b4adf1c24edb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#105;&#110;&#101;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#32;&#115;&#105;&#103;&#110;&#115;&#32;&#114;&#101;&#118;&#101;&#114;&#115;&#101;&#100;&#32;&#116;&#104;&#101;&#105;&#114;&#32;&#100;&#105;&#114;&#101;&#99;&#116;&#105;&#111;&#110;&#46;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"347\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"fs-id1168345261900\">When we divide or multiply an inequality by a positive number, the inequality sign stays the same. When we divide or multiply an inequality by a negative number, the inequality sign reverses.<\/p>\n<p id=\"fs-id1168345297633\">Here are the Division and Multiplication Properties of Inequality for easy reference.<\/p>\n<div id=\"fs-id1168345450893\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Division and Multiplication Properties of Inequality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6411\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.40.23-PM.png\" alt=\"\" width=\"1956\" height=\"1148\" \/><\/p>\n<\/div>\n<\/div>\n<p><span style=\"text-align: initial; font-size: 14pt;\">When we <\/span><strong style=\"text-align: initial; font-size: 14pt;\" data-effect=\"bold\">divide or multiply<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> an inequality by a:<\/span><\/p>\n<\/div>\n<\/div>\n<ul id=\"fs-id1168341864334\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">positive<\/strong> number, the inequality stays the <strong data-effect=\"bold\">same<\/strong>.<\/li>\n<li><strong data-effect=\"bold\">negative<\/strong> number, the inequality <strong data-effect=\"bold\">reverses<\/strong>.<\/li>\n<\/ul>\n<div id=\"fs-id1168345251297\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345292807\" data-type=\"exercise\">\n<div id=\"fs-id1168345526626\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345450214\" data-type=\"problem\">\n<p id=\"fs-id1168345284577\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-190eea1fe2fb9d508969d8a6808f6a1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-663d228316bfd115aace82901fc82ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345692782\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168465351020\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 7y is less than 42. One line down to the left, the instructions say: \u201cDivide both sides of the inequality by 7. Since 7 is greater than 0, the inequality stays the same.\u201d To the right of this instruction is the original inequality divided by 7 on both sides: 7y over 7 is less than 42 over 7. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality y is less than 6. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from 4 to 7, with tick marks at each integer. The inequality y is less than 6 is graphed on the number line, with an open parenthesis at y equals 6, and a red line extending from there to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma 6, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465351054\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Divide both sides of the inequality by 7.<span data-type=\"newline\"><br \/>\n<\/span>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, the inequality stays the same.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168465351071\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465089167\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168465089185\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168465089202\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_031e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345526626\" data-type=\"problem\">\n<p id=\"fs-id1168345297541\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345522080\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d89bc25e3a6c2eb689f9d5120ec4aaae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345474658\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345743063\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1168345388293\" data-type=\"media\" data-alt=\"This figure is a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is greater than 8 is graphed on the number line, with an open parenthesis at c equals 8, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_032_img_new.jpg\" alt=\"This figure is a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is greater than 8 is graphed on the number line, with an open parenthesis at c equals 8, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345287560\" data-type=\"problem\">\n<p id=\"fs-id1168345455350\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cfb7d29f36dd85789e22fa667c46d85c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#97;&#92;&#103;&#101;&#32;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -3px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1168345422084\" data-type=\"solution\">\n<table id=\"eip-id1168460536424\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality negative 10a is greater than or equal to 50. One line down to the left, the instructions say: \u201cDivide both sides of the inequality by negative 10. Since negative 10 is less than 0, the inequality reverses.\u201d To the right of this instruction is the original inequality divided by negative 10 on both sides: negative 10a over negative 10 is greater than or equal to 50 over negative 10, with the greater than or equal to sign written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality a is less than or equal to negative 5. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 7 to negative 4, with tick marks at each integer. The inequality a is less then or equal to negative 5 is graphed on the number line, with an open bracket at a equals negative 5, and a red line extending from there to the left. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma negative 5, bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168460536420\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Divide both sides of the inequality by \u221210.<span data-type=\"newline\"><br \/>\n<\/span>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, the inequality reverses.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168462716164\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168462716199\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168462716216\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168462716233\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_034e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342181668\" data-type=\"problem\">\n<p id=\"fs-id1168342181516\">Solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168342040546\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3cc5aabe230510cce2441bf6cfd25333_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345388596\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345250203\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1168345250204\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 6 to negative 3 with tick marks for each integer. The inequality q is greater than negative 4 is graphed on the number line, with an open parenthesis at q equals negative 4, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 4 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_035_img_new.jpg\" alt=\"This figure is a number line ranging from negative 6 to negative 3 with tick marks for each integer. The inequality q is greater than negative 4 is graphed on the number line, with an open parenthesis at q equals negative 4, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 4 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345196580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345644359\" data-type=\"exercise\">\n<h1>Solving Inequalities<\/h1>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345695536\" data-type=\"note\">\n<p id=\"fs-id1168345622665\">Sometimes when solving an inequality, the variable ends up on the right. We can rewrite the inequality in reverse to get the variable to the left.<\/p>\n<div data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6412 alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/Screenshot-2021-06-15-at-1.40.44-PM.png\" alt=\"\" width=\"369\" height=\"29\" \/><\/div>\n<p>&nbsp;<\/p>\n<p id=\"fs-id1168342156004\">Think about it as \u201cIf Xavier is taller than Alex, then Alex is shorter than Xavier.\u201d<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345424531\" data-type=\"problem\">\n<p id=\"fs-id1168345500479\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae8c3958b12fc2329d7aff2a69770ce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"19\" style=\"vertical-align: -6px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345461433\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168462821337\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality negative 20 is less than four-fifths u. One line down to the left, the instructions say: \u201cMultiply both sides of the inequality by 5\/4. Since 5\/4 is greater than 0, the inequality stays the same.\u201d To the right of this instruction is the original inequality multiplied by 5\/4 on both sides: 5\/4 times negative 20 is less than 5\/4 times four-fifths u. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality negative 25 is less than u. One more line down on the left, the instructions say: \u201cRewrite with the variable on the left.\u201d To the right of this sentence is the inequality u is greater than negative 25. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 26 to negative 23, with tick marks at each integer. The inequality u is greater than negative 25 is graphed on the number line, with an open parenthesis at u equals negative 25, and a red line extending from there to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative 25 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168462821374\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Multiply both sides of the inequality by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>&gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, the inequality stays the same.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168462821398\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168462821436\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the variable on the left.<\/td>\n<td><span id=\"eip-id1168462821453\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168462821471\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168462821488\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_037f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345742335\" data-type=\"problem\">\n<p id=\"fs-id1168345742481\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1168345431017\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-111542a5579f1fd9f62694b0f88f5cd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#92;&#108;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345676986\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345527811\" data-type=\"media\" data-alt=\"This figure shows the inequality m is greater than or equal to 64. Below this inequality is a number line ranging from 63 to 67 with tick marks for each integer. The inequality m is greater than or equal to 64 is graphed on the number line, with an open bracket at m equals 64, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 64 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_038_img_new.jpg\" alt=\"This figure shows the inequality m is greater than or equal to 64. Below this inequality is a number line ranging from 63 to 67 with tick marks for each integer. The inequality m is greater than or equal to 64 is graphed on the number line, with an open bracket at m equals 64, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 64 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345483994\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345418989\" data-type=\"exercise\">\n<div id=\"fs-id1168345655058\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345256384\" data-type=\"problem\">\n<p id=\"fs-id1168345448052\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d312a98624cf94a94b40ea1dc8d139a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#116;&#125;&#123;&#45;&#50;&#125;&#92;&#103;&#101;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -6px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345427063\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168460952556\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality t over negative 2 is greater than or equal two 8. One line down to the left, the instructions say: \u201cMultiply both sides of the inequality by negative 2. Since negative 2 is less than 0, the inequality reverses.\u201d To the right of this instruction is the original inequality multiplied by negative 2 on both sides: negative 2 times t over negative 2, with t over negative 2 in parentheses, is less than or equal to negative 2 times 8, with the is less than or equal to symbol written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality t is less than or equal to negative 16. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 18 to negative 15, with tick marks at each integer. The inequality t is less than or equal to negative 16 is graphed on the number line, with an open bracket at t equals negative 16, and a red line extending from the bracket to the left. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: parenthesis, negative infinity comma negative 16, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168463908074\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Multiply both sides of the inequality by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, the inequality reverses.<\/td>\n<td data-valign=\"bottom\"><span id=\"eip-id1168463908095\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461208480\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461208497\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168461555572\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_040e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345508568\" data-type=\"problem\">\n<p id=\"fs-id1168345508570\">Solve the inequality, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<p id=\"fs-id1167265668550\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1d274cdf73ceec193787aa0aae0fc5ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#107;&#125;&#123;&#45;&#49;&#50;&#125;&#92;&#108;&#101;&#32;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"67\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345655073\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345449801\" data-type=\"media\" data-alt=\"This figure shows the inequality k is greater than or equal to negative 180. Below this inequality is a number line ranging from negative 181 to negative 177 with tick marks for each integer. The inequality k is greater than or equal to negative 180 is graphed on the number line, with an open bracket at n equals negative 180, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, negative 180 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_041_img_new.jpg\" alt=\"This figure shows the inequality k is greater than or equal to negative 180. Below this inequality is a number line ranging from negative 181 to negative 177 with tick marks for each integer. The inequality k is greater than or equal to negative 180 is graphed on the number line, with an open bracket at n equals negative 180, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, negative 180 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341960485\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Solve Inequalities That Require Simplification<\/h1>\n<p id=\"fs-id1168345398559\">Most inequalities will take more than one step to solve. We follow the same steps we used in the general strategy for solving linear equations, but be sure to pay close attention during multiplication or division.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345436018\" data-type=\"problem\">\n<p id=\"fs-id1168345436021\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c521a31e93d7551a64687984c5d195f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#92;&#108;&#101;&#32;&#57;&#109;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" style=\"vertical-align: -3px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345287544\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168465372853\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 4m is less than or equal to 9m plus 17. One line down to the left, the instructions say: \u201cSubtract 9m from both sides to collect the variables on the left.\u201d To the right of this sentence is the original inequality with 9m subtracted from both sides: 4m minus 9m is less than or equal to 9m minus 9m plus 17. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality negative 5m is less than or equal to 17. Another line down on the left, the instructions say: \u201cDivide both sides of the inequality by negative 5, and reverse the inequality.\u201d To the right of this instruction is the original inequality divided by negative 5 on both sides: negative 5m over negative 5 is greater than or equal to 17 over negative 5, with the is greater than or equal to symbol written in red. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality m is greater than or equal to negative 17\/5. Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this sentence is a number line ranging from negative 5 to negative 2, with tick marks at each integer. The inequality m is greater than or equal to negative 17\/5 is graphed on the number line, with an open bracket at m equals negative 17\/5 (written in), and a red line extending from the bracket to the right. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the notation: bracket, negative 17\/5 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168465372838\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-258b533c54c06975f9442ccad739b8c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"24\" style=\"vertical-align: 0px;\" \/> from both sides to collect the variables on the left.<\/td>\n<td><span id=\"eip-id1168465372882\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465372899\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides of the inequality by \u22125, and reverse the inequality.<\/td>\n<td><span id=\"eip-id1168465372917\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168465372934\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"fs-id1169145576659\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td><span id=\"eip-id1168465372951\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_043g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345374096\" data-type=\"problem\">\n<p id=\"fs-id1168345374098\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc9233ade9cb5a97e6ad005da0736e36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#113;&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#49;&#55;&#101;&#109;&#125;&#125;&#92;&#103;&#101;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#49;&#55;&#101;&#109;&#125;&#125;&#55;&#113;&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#49;&#55;&#101;&#109;&#125;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#104;&#115;&#112;&#97;&#99;&#101;&#123;&#48;&#46;&#49;&#55;&#101;&#109;&#125;&#125;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -4px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345446027\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345255758\" data-type=\"media\" data-alt=\"This figure shows the inequality q is less than or equal to 23\/4. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality q is less than or equal to 23\/4 is graphed on the number line, with an open bracket at q equals 23\/4 (written in), and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 23\/4, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_044_img_new.jpg\" alt=\"This figure shows the inequality q is less than or equal to 23\/4. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality q is less than or equal to 23\/4 is graphed on the number line, with an open bracket at q equals 23\/4 (written in), and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 23\/4, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345325808\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345433462\" data-type=\"exercise\">\n<div id=\"fs-id1168345552417\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345416793\" data-type=\"problem\">\n<p id=\"fs-id1168345385584\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2a447c2d18858d0ddd5fbb5162766bb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#112;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9673e55455c3966b994cf9b1cec0df68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168341892598\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461313752\" style=\"height: 244px; width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 8p plus 3 times p minus 12, with p minus 12 in parentheses, is greater than 7p minus 28. One line down to the left, the instructions say: \u201cSimplify each side as much as possible. Distribute.\u201d To the right of this instruction is the inequality with 3 distributed through the parentheses: 8p plus 3p minus 36 is greater than 7p minus 28. One more line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 11p minus 36 is greater than 7p minus 28. Another line down on the left, the instructions say: \u201cSubtract 7p from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 7p subtracted from both sides: 11p minus 36 minus 7p is greater than 7p minus 28 minus 7p. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality 4p minus 36 is greater than negative 28. Another line down on the left, the instructions say: \u201cAdd 36 to both sides to collect the constants on the right.\u201d To the right of this sentence is the same inequality with 36 added to both sides: 4p minus 36 plus 36 is greater than negative 28 plus 36. Another line down on the left, the instructions say: \u201cSimpify.\u201d To the right of this instruction is the inequality 4p is greater than 8. One more line down on the left, the instructions say: \u201cDivide both sides of the inequality by 4; the inequality stays the same.\u201d To the right of this instruction is the inequality divided by 4 on both sides: 4p over 4 is greater than 8 over 4. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality p is greater than 2. Another line down to the left, the instructions say: \u201cGraph the solution on the number line. Write the solution in interval notation.\u201d To the right of this instruction is a number line ranging from 0 to 3, with tick marks at each integer. The inequality p is greater than 2 is graphed on the number line, with an open parenthesis at p equals 2, and a red line extending from the parenthesis to the right. Below the number line is the notation: parenthesis, 2 comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify each side as much as possible.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2a447c2d18858d0ddd5fbb5162766bb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#112;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9673e55455c3966b994cf9b1cec0df68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Distribute.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2ec8b0686b8ad8bc07e40f9cdb6dbf3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#112;&#43;&#51;&#112;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9673e55455c3966b994cf9b1cec0df68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Combine like terms.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f6e0370e0758d6e9f73cce0fc23f3850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#49;&#112;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9673e55455c3966b994cf9b1cec0df68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-58bfcd4057f1d18a954d8b481b113d96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> from both sides to collect the variables on the left.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4c0bc67c21607a1cc852ed2fca6510ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#49;&#112;&#45;&#51;&#54;&#45;&#55;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0cedaeb6c9e3d9ab0bfa8ca0ae20f4b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#45;&#50;&#56;&#45;&#55;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1fc79035b74892b71b7f1bc7d983498b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#112;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7eaefbab9f26b55d0afa7f1689372c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Add 36 to both sides to collect the constants on the right.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6af15a7ce5b95b6b81b466005eec4f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#112;&#45;&#51;&#54;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ffe1ac9cde27ebad62746c8789eeb8bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b270fea8befc5caaeec947fd23635f71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 369.406px;\">Divide both sides of the inequality by 4; the inequality stays the same.<\/td>\n<td style=\"height: 30px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6198c9c7120181239ee5f7c885a537c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#112;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"14\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2e61c14568e7048877026c57ab0b19c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-37c18fd33fc9f0ce9fdca45bc73411ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"height: 40px; width: 369.406px;\">Graph the solution on the number line.<\/td>\n<td style=\"height: 40px; width: 308.406px;\"><span id=\"eip-id1168463856754\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_046a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 369.406px;\">Write the solution in interal notation.<\/td>\n<td style=\"height: 14px; width: 308.406px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b3103559f9a65200f03c9dd13b132df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345455047\" data-type=\"problem\">\n<p id=\"fs-id1168345455049\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8493dc8904aab8b223e8f3fc4187ed81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f652338fdb0d0e32289c915020153726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -4px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345742714\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168342181624\" data-type=\"media\" data-alt=\"This figure shows the inequality y is greater than negative 6. Below this inequality is a number line ranging from negative 7 to negative 3 with tick marks for each integer. The inequality y is greater than negative 6 is graphed on the number line, with an open parenthesis at y equals negative 6, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 6 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_047_img_new.jpg\" alt=\"This figure shows the inequality y is greater than negative 6. Below this inequality is a number line ranging from negative 7 to negative 3 with tick marks for each integer. The inequality y is greater than negative 6 is graphed on the number line, with an open parenthesis at y equals negative 6, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 6 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"text-align: initial; font-size: 14pt;\">Just like some equations are identities and some are contradictions, inequalities may be identities or contradictions, too. We recognize these forms when we are left with only constants as we solve the inequality. If the result is a true statement, we have an identity. If the result is a false statement, we have a contradiction.<\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345387524\" data-type=\"problem\">\n<p id=\"fs-id1168345449878\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23b99696274ad46cf094e7d8dce6be72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa7bdd0c38fc8d6ad59802996edc6595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345744775\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168461237712\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality 8x minus 2 times 5 minus x, with 5 minus x in parentheses, is less than 4 times x plus 9, with x plus 9 in parentheses, plus 6x. One line down to the left, the instructions say: \u201cSimplify each side as much as possible. Distribute.\u201d To the right of this instruction is the inequality with 2 distributed through the parentheses on the left side and 4 distributed through the parentheses on the right: 8x minus 10 plus 2x is less than 4x plus 36 plus 6x. One more line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 10x minus 10 is less than 10x plus 36. Another line down on the left, the instructions say: \u201cSubtract 10x from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 10x subtracted from both sides: 10x minus 10 minus 10x is less than 10x plus 36 minus 10x. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality negative 10 is less than 36. Another line down on the left, the instructions say: \u201cThe x\u2019s are gone, and we have a true statement.\u201d To the right is the text: \u201cThe inequality is an identity. The solution is all real numbers.\u201d Another line down to the left, the instructions say: \u201cGraph the solution on the number line. Write the solution in interval notation.\u201d To the right of this instruction is a number line ranging from negative 1 to 2, with tick marks at each integer. The inequality is graphed on the number line. Because this is an identity and the solution is all real numbers, the graph is a red line extending in both directions on the number line. Below the number line is the notation: parenthesis, negative infinity comma infinity, parenthesis.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Simplify each side as much as possible.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23b99696274ad46cf094e7d8dce6be72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa7bdd0c38fc8d6ad59802996edc6595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8eaad9a4db2feede4b7242b7a2728fa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#49;&#48;&#43;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"99\" style=\"vertical-align: -2px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b6f28150dfac9f3e109b6fa3295ad87b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#54;&#43;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"99\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a9d12ea2ba624742643ea96bfd32ed55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fcbc717c15b21b6c850fd829cd396c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-405a623e7d2a6832578e529d3677c15a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> from both sides to collect the variables on the left.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-faf2ed5a3dbfaf6e167426e1773e3d4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#45;&#49;&#48;&#45;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"116\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7bff6dfc04ad14d09b9b18d5fa10d9c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#43;&#51;&#54;&#45;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"116\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a26f73071c6f6ebe5a999d439bc733c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>\u2019s are gone, and we have a true statement.<\/td>\n<td data-align=\"center\">The inequality is an identity.<span data-type=\"newline\"><br \/>\n<\/span>The solution is all real numbers.<\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461228510\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_049a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3114f29e6d5b912bf7739fb2e4deeeb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#44;&#92;&#105;&#110;&#102;&#116;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342167586\" data-type=\"problem\">\n<p id=\"fs-id1168345442902\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bbb95220dbb2b0f15cce3e589acc4b63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#98;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2af4f40796d30625b1a9804ede36fe1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345397967\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168341963297\" data-type=\"media\" data-alt=\"This figure shows an inequality that is an identity. Below this inequality is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. The inequality is also written in interval notation as parenthesis, negative infinity comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_050_img_new.jpg\" alt=\"This figure shows an inequality that is an identity. Below this inequality is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. The inequality is also written in interval notation as parenthesis, negative infinity comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341975166\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341975169\" data-type=\"exercise\">\n<div id=\"fs-id1168345695450\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341959544\" data-type=\"problem\">\n<p id=\"fs-id1168341959546\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4b1ab3bfbaf3ebc4958afc2eec4aee9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#97;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8417912a89b4f14c759dff847f90c28f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#52;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345423625\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463871077\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the inequality one-third a minus one-eighth a is greater than five-twenty-fourths a plus 3\/4. One line down to the left, the instructions say: \u201cMultiply both sides by the LCD, 24, to clear the fractions.\u201d To the right of this instruction is the inequality multiplied by 24 on both sides: 24 times one-third a minus one-eighth a, with one-third a minus one-eighth a in parentheses, is greater than 24 times five-twenty-fourths a plus \u00be, with five-twenty-fourths a plus \u00be in parentheses, and \u201c24 times\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the inequality 8a minus 3a is greater than 5a plus 18. Another line down to the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the inequality 5a is greater than 5a plus 18. Another line down on the left, the instructions say: \u201cSubtract 5a from both sides to collect the variables on the left.\u201d To the right of this sentence is the same inequality with 5a subtracted from both sides: 5a minus 5a is greater than 5a minus 5a plus 18. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the inequality 0 is greater than 18. Another line down on the left, the instructions say: \u201cThe statement is false!\u201d To the right is the text: \u201cThe inequality is a contradiction.\u201d Another line down to the left, the instructions say: \u201cGraph the solution on the number line.\u201d To the right of this instruction is a number line ranging from negative 1 to 2, with tick marks at each integer. No inequality is graphed on the number line. One more line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this sentence is the text: \u201cThere is no solution.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168459278426\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by the LCD, 24, to clear the fractions.<\/td>\n<td><span id=\"eip-id1168459278443\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168461145691\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168461804210\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9360ef9fb862d7bf0e669eb7b4606fea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> from both sides to collect the variables on the left.<\/td>\n<td><span id=\"eip-id1168461804234\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"fs-id1169147708868\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The statement is false!<\/td>\n<td>The inequality is a contradiction.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>There is no solution.<\/td>\n<\/tr>\n<tr>\n<td>Graph the solution on the number line.<\/td>\n<td><span id=\"eip-id1168461201953\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_052g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the solution in interval notation.<\/td>\n<td>There is no solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345251538\" data-type=\"problem\">\n<p id=\"fs-id1168345329045\">Solve the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6143daefdd86883fd4898cd33e2ff9a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-94f27e5492f3883afad4c2c1644c81ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/>, graph the solution on the number line, and write the solution in interval notation.<\/p>\n<\/div>\n<div id=\"fs-id1168345217894\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345647699\" data-type=\"media\" data-alt=\"This figure shows an inequality that is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. No inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_053_img_new.jpg\" alt=\"This figure shows an inequality that is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. No inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345500407\" class=\"bc-section section\" data-depth=\"1\">\n<h1>Translate to an Inequality and Solve<\/h1>\n<p id=\"fs-id1168345253149\">To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. Some words are easy, like \u2018more than\u2019 and \u2018less than\u2019. But others are not as obvious.<\/p>\n<p id=\"fs-id1168342101872\">Think about the phrase \u2018at least\u2019 \u2013 what does it mean to be \u2018at least 21 years old\u2019? It means 21 or more. The phrase \u2018at least\u2019 is the same as \u2018greater than or equal to\u2019.<\/p>\n<p id=\"fs-id1168345423772\"><a class=\"autogenerated-content\" href=\"#fs-id1168345688476\">(Figure)<\/a> shows some common phrases that indicate inequalities.<\/p>\n<table id=\"fs-id1168345688476\" class=\"grid\" summary=\"This figure is a table with four columns and five rows. The first row, which is a header row, contains inequality symbols. Starting from the first cell to the left, the symbols left to right are: the symbols are is greater than, is greater than or equal to, is less than, and is less than or equal to. Below the header row in the first column are words or phrases that indicate the symbol is greater than. Starting from the second row and going down, these words and phrases are: \u201cis greater than,\u201d \u201cis more than,\u201d \u201cis larger than,\u201d and \u201cexceeds.\u201d Below the header row in the second column are phrases that indicate the symbol is greater than or equal to. Starting from the second row and going down, these phrases are: \u201cgreater than or equal to,\u201d \u201cis at least,\u201d \u201cis no less than,\u201d and \u201cis the minimum.\u201d Below the header row in the third column are phrases that indicate the symbol is less than. Starting from the second row and going down, these phrases are: \u201cis less than,\u201d \u201cis smaller than,\u201d \u201chas fewer than,\u201d and \u201cis lower than.\u201d Below the header row in the last column are phrases that indicate the symbol is less than or equal to. Starting from the second row and going down, these phrases are: \u201cis less than or equal to,\u201d \u201cis at most,\u201d \u201cis no more than,\u201d and \u201cis the maximum.\u201d\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"middle\" data-align=\"center\">&gt;<\/th>\n<th data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2bed2a7b3a4cb8554a7ceb3c94e90a24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"12\" style=\"vertical-align: -3px;\" \/><\/th>\n<th data-valign=\"middle\" data-align=\"center\">&lt;<\/th>\n<th data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-54e2b165150917469474a6d203f27e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"12\" style=\"vertical-align: -3px;\" \/><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is greater than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is greater than or equal to<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is less than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is less than or equal to<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is more than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is at least<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is smaller than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is at most<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">is larger than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is no less than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">has fewer than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is no more than<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">exceeds<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is the minimum<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is lower than<\/td>\n<td data-valign=\"middle\" data-align=\"left\">is the maximum<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345720316\" data-type=\"problem\">\n<p id=\"fs-id1168345251022\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169751872347\">Twelve times <em data-effect=\"italics\">c<\/em> is no more than 96.<\/p>\n<\/div>\n<div id=\"fs-id1168345416357\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463007039\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the math phrase \u201cTwelve times c is no more than 96, with \u201cis no more than\u201d highlighted with a bracket. One line down to the left, the instructions say: \u201cTranslate.\u201d To the right of this instruction is the inequality 12c is less than or equal to 96. One more line down on the left, the instructions say: \u201cSolve\u2014divide both sides by 12.\u201d To the right of this sentence is the same inequality divided by 12 on both sides: 12c over 12 is less than or equal to 96 over 12. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality c is less than or equal to 8. Another line down to the left, the instructions say: \u201cWrite the solution in interval notation.\u201d To the right of this instruction is the inequality in interval notation: parenthesis, negative infinity comma 8. One more line down on the left, the instructions say: \u201cGraph on the number line.\u201d To the right of this sentence a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is less than or equal to 8 is graphed on the number line, with an open bracket at c equals 8, and a dark line extending from the parenthesis to the left.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td colspan=\"0\"><span id=\"eip-id1168463007056\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve\u2014divide both sides by 12.<\/td>\n<td><span id=\"eip-id1168463007073\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463007090\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463007108\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph on the number line.<\/td>\n<td><span id=\"eip-id1168463007125\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_055e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345424285\" data-type=\"problem\">\n<p id=\"fs-id1168345424288\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1168342156018\">Twenty times <em data-effect=\"italics\">y<\/em> is at most 100<\/p>\n<\/div>\n<div id=\"fs-id1168345425365\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345425368\" data-type=\"media\" data-alt=\"This figure shows the inequality 20y is less than or equal to 100, and then its solution: y is less than or equal to 5. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality y is less than or equal to 5 is graphed on the number line, with an open bracket at y equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_056_img_new.jpg\" alt=\"This figure shows the inequality 20y is less than or equal to 100, and then its solution: y is less than or equal to 5. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality y is less than or equal to 5 is graphed on the number line, with an open bracket at y equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342079179\" data-type=\"problem\">\n<p id=\"fs-id1168342079181\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169751893803\">Thirty less than <em data-effect=\"italics\">x<\/em> is at least 45.<\/p>\n<\/div>\n<div id=\"fs-id1168345743107\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463004929\" style=\"width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the math phrase \u201cThirty less than x is at least 45, with \u201cis at least\u201d highlighted with a bracket. One line down to the left, the instructions say: \u201cTranslate.\u201d To the right of this instruction is the inequality x minus 30 is greater than or equal to 45. One more line down on the left, the instructions say: \u201cSolve\u2014add 30 to both sides.\u201d To the right of this sentence is the same inequality with 30 added to both sides: x minus 30 plus 30 is greater than or equal to 45 plus 30, with \u201cplus 30\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right is the inequality x is greater than or equal to 75. Another line down to the left, the instructions say: \u201cWrite in interval notation.\u201d To the right of this instruction is the inequality in interval notation: bracket, 75 comma infinity, parenthesis. One more line down on the left, the instructions say: \u201cGraph on the number line.\u201d To the right of this sentence is a number line ranging from 74 to 77 with tick marks for each integer. The inequality x is greater than or equal to 75 is graphed on the number line, with an open bracket at x equals 75, and a red line extending to the right of the bracket.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td><span id=\"eip-id1168463004966\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Solve\u2014add 30 to both sides.<\/td>\n<td><span id=\"eip-id1168463004983\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168463005000\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write in interval notation.<\/td>\n<td><span id=\"eip-id1168463005017\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Graph on the number line.<\/td>\n<td><span id=\"eip-id1168463005035\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_058e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345530275\" data-type=\"problem\">\n<p id=\"fs-id1168345259208\">Translate and solve. Then write the solution in interval notation and graph on the number line.<\/p>\n<p id=\"fs-id1169754028949\">Nineteen less than <em data-effect=\"italics\">p<\/em> is no less than 47<\/p>\n<\/div>\n<div id=\"fs-id1168345196869\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><span id=\"fs-id1168345407099\" data-type=\"media\" data-alt=\"This figure shows the inequality p minus 19 is greater than or equal to 47, and then its solution: p is greater than or equal to 66. Below this inequality is a number line ranging from 65 to 69 with tick marks for each integer. The inequality p is greater than or equal to 66 is graphed on the number line, with an open bracket at p equals 66, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 66 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_059_img_new.jpg\" alt=\"This figure shows the inequality p minus 19 is greater than or equal to 47, and then its solution: p is greater than or equal to 66. Below this inequality is a number line ranging from 65 to 69 with tick marks for each integer. The inequality p is greater than or equal to 66 is graphed on the number line, with an open bracket at p equals 66, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 66 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul>\n<li><strong data-effect=\"bold\">Subtraction Property of Inequality<\/strong><span data-type=\"newline\"><br \/>\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d31c40c474097c761328f414cd29414b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"39\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6da77e5c6e3ae3f4e2267c680fea3c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"37\" style=\"vertical-align: 0px;\" \/> and<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d31c40c474097c761328f414cd29414b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"39\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11c6adb5100efd0caff58f74f8683bb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#45;&#99;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Addition Property of Inequality<\/strong><span data-type=\"newline\"><br \/>\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ed713d824da28fe5fbf02e7894f7be90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: -2px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8bd10e63b5b942621f44b4893747f9e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"37\" style=\"vertical-align: -2px;\" \/> and<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ed713d824da28fe5fbf02e7894f7be90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2c26e81df526218cdff7c2b8222d266_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#43;&#99;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Division and Multiplication Properties of Inequalit<\/strong><strong data-effect=\"bold\">y<\/strong><span data-type=\"newline\"><br \/>\n<\/span> For any numbers a, b, and c,<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b99f893b0361caf1e8228b98c1855a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce368c1c836cac62138c7961c648391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"6\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fe68776986c55a6eacdb12c5a99552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f26f32254e5f6a1cb50d61ed56b718e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b99f893b0361caf1e8228b98c1855a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce368c1c836cac62138c7961c648391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"6\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fe68776986c55a6eacdb12c5a99552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f26f32254e5f6a1cb50d61ed56b718e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b99f893b0361caf1e8228b98c1855a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce368c1c836cac62138c7961c648391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"6\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fe68776986c55a6eacdb12c5a99552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f26f32254e5f6a1cb50d61ed56b718e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b99f893b0361caf1e8228b98c1855a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce368c1c836cac62138c7961c648391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"6\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fe68776986c55a6eacdb12c5a99552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f26f32254e5f6a1cb50d61ed56b718e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span><\/li>\n<li>When we <strong data-effect=\"bold\">divide or multiply<\/strong> an inequality by a:\n<ul id=\"fs-id1168345543646\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">positive<\/strong> number, the inequality stays the <strong data-effect=\"bold\">same<\/strong>.<\/li>\n<li><strong data-effect=\"bold\">negative<\/strong> number, the inequality <strong data-effect=\"bold\">reverses<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>2.5 Exercise Set<\/h1>\n<p id=\"fs-id1169749983130\">In the following exercises, graph each inequality on the number line.<\/p>\n<ol class=\"twocolumn\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7fbeff4bf1f5a9077e4fa8e1ef53b535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#92;&#103;&#101;&#32;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -3px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01a21253101daa842e76248d87471fcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2d49bbfc8ad57b9d1026338a97f6bf6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1168345450007\">In the following exercises, graph each inequality on the number line and write in interval notation.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c49d9cc64b220a8227bfc035ca02696a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#45;&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"70\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4096541a73965dde20098d399384a65b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b157a9b63bb99ace04045920c37207c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#108;&#101;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d2c179d195826a7e574cb8027015b67c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#103;&#101;&#32;&#45;&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"70\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9a2cb7751ad736431e03a3f373debdd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div id=\"fs-id1168345442027\" data-type=\"exercise\">\n<div id=\"fs-id1168345442029\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<\/div>\n<div id=\"fs-id1168345454367\" data-type=\"exercise\">\n<div id=\"fs-id1168345454369\" data-type=\"problem\">\n<ol class=\"twocolumn\" start=\"5\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-20802ac030ec4b16f55c50df2c61e3bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#45;&#52;&#53;&#92;&#108;&#101;&#32;&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bda5d87a9f89cc4829a859c8ece73a28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b1a80bd17ee1668ec1d0504d758ae876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#92;&#103;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"73\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aa14aab9bd9732208e802da4c854dd66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e28c4bb85b98bec0c931a7586c3b9ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341861931\" data-type=\"exercise\">\n<div id=\"fs-id1168341861933\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"9\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bfee8365bfa4aa582b53f6b63fceb63e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1f11c6e846ac2fe8cea2c6e472ea6458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a6cf1e761b5c92e5af83a3814c6ec27f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#115;&#92;&#103;&#101;&#32;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65a1e7421c636dfb0f2e58c383418613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#118;&#92;&#108;&#101;&#32;&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df85e73b3f95277d2e37bfb40df48b60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-077994c193e366e731b386b8503f548d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-89bc2c119dcafc9b555c6b2841530d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1e15e8976465a75f53ffd518a099a29f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71352fea45d0777c2b59362ca717a6d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#125;&#103;&#92;&#108;&#101;&#32;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-77820316a7065484ff09a0d776a5f7bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#45;&#49;&#48;&#125;&#92;&#103;&#101;&#32;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"68\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ca7f59afc021934b3158e53f5df0dd45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#113;&#125;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a7269e0c0ac47e433419dde10d6ec669_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7eaefbab9f26b55d0afa7f1689372c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3dcefca6de3ac22b1f4fe43af26c34eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;&#92;&#108;&#101;&#32;&#45;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345543040\" data-type=\"exercise\">\n<div id=\"fs-id1168345543042\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<\/div>\n<div id=\"fs-id1168345449792\" data-type=\"exercise\">\n<div id=\"fs-id1168345449795\" data-type=\"problem\">\n<ol class=\"twocolumn\" start=\"19\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f0d1bad3f631d9b57fbec824eb1554ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#117;&#92;&#108;&#101;&#32;&#56;&#117;&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-db086278b031572750fe50587476a487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-106320743ef00a8ce075c612a6ae4d60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#112;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a760da58a847f9a159bd54dc10e92f2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09d472f831a70433425c5363a9538639_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae40c4e35f79baedd4905b58f9d323d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#107;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#103;&#101;&#32;&#55;&#107;&#45;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"176\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-692dbe98f08bd9d5211ef044706d7bab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#110;&#45;&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#32;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"249\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc5ba67c1e04ea1f4bed26e4686af0aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#117;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#117;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#103;&#101;&#32;&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"255\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b219573c7d8554f7e4efe8bed171d63d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#97;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5937db0823c8d2fbbed72a0af614f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c93077631ecd029c6eabb1ae74b87e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#118;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#118;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#32;&#49;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"259\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345726340\" data-type=\"exercise\">\n<div id=\"fs-id1168345726342\" data-type=\"problem\"><span style=\"orphans: 1; text-align: initial; font-size: 14pt;\">In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"27\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-236410a06bde0a55b514e954b2e164e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#107;&#92;&#103;&#101;&#32;&#45;&#55;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8a72a0ecee9cf909928b4906c1b2248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#113;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#45;&#51;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-261551a33466b36bed040ae41b1de785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#113;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4c2427179cd472b6cba3d4fafdf3f727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#56;&#125;&#121;&#92;&#108;&#101;&#32;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"93\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3b21df65a769b2993caa58faedcf53e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#43;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e04e4698afac1925c1fb3437f5973900_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-99f68e42394e41343240f1282a41f3b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#49;&#51;&#125;&#92;&#108;&#101;&#32;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345511366\" data-type=\"exercise\">\n<div id=\"fs-id1168345511368\" data-type=\"problem\"><span style=\"font-size: 14pt; text-align: initial; orphans: 1;\">In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"32\">\n<li>Ninety times <em data-effect=\"italics\">c<\/em> is less than 450.<\/li>\n<li>Ten times <em data-effect=\"italics\">y<\/em> is at most <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a3a0e41146ca640a756037e5b866d22e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<li>Six more than <em data-effect=\"italics\">k<\/em> exceeds 25.<\/li>\n<li>Twelve less than <em data-effect=\"italics\">x<\/em> is no less than 21.<\/li>\n<li>Negative two times <em data-effect=\"italics\">s<\/em> is lower than 56.<\/li>\n<li>Fifteen less than <em data-effect=\"italics\">a<\/em> is at least <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The maximum height, <em data-effect=\"italics\">h<\/em>, of a fighter pilot is 77 inches. Write this as an inequality.<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345287059\" data-type=\"exercise\">\n<h1>Answers<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 1633px;\">\n<tbody>\n<tr style=\"height: 329px;\">\n<td style=\"width: 33.3333%; height: 329px;\"><span class=\"token\">1. <\/span><\/p>\n<p><span class=\"token\">a.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345408756\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 1 is graphed on the number line, with an open parenthesis at x equals 1, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_204_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 1 is graphed on the number line, with an open parenthesis at x equals 1, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">b.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168341854168\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the left of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_205_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">c.<\/span><span id=\"fs-id1168345255064\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 3 is graphed on the number line, with an open bracket at x equals negative 3, and a dark line extending to the right of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_206_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 3 is graphed on the number line, with an open bracket at x equals negative 3, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 329px;\">2.<\/p>\n<p><span class=\"token\">a.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345415049\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 0 is graphed on the number line, with an open bracket at x equals 0, and a dark line extending to the left of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_210_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 0 is graphed on the number line, with an open bracket at x equals 0, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">b.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345650393\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 4 is graphed on the number line, with an open parenthesis at x equals negative 4, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_211_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 4 is graphed on the number line, with an open parenthesis at x equals negative 4, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span data-type=\"newline\">c.<br \/>\n<\/span><span id=\"fs-id1168345538820\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_212_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 329px;\">3.<\/p>\n<p><span class=\"token\">a.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345650400\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the right of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, 3 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_216_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the right of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, 3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">b.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345431173\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 0.5 is graphed on the number line, with an open bracket at x equals negative 0.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 0.5, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_217_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 0.5 is graphed on the number line, with an open bracket at x equals negative 0.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 0.5, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">c.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345443821\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1\/3 is graphed on the number line, with an open bracket at x equals 1\/3 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 1\/3 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_218_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1\/3 is graphed on the number line, with an open bracket at x equals 1\/3 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 1\/3 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 361px;\">\n<td style=\"width: 33.3333%; height: 361px;\">4.<\/p>\n<p><span class=\"token\">a.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168342181524\" data-type=\"media\" data-alt=\"This figure is a number line with tick marks. The inequality x is less than or equal to 5 is graphed on the number line, with an open bracket at x equals 5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 5, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_222_img_new.jpg\" alt=\"This figure is a number line with tick marks. The inequality x is less than or equal to 5 is graphed on the number line, with an open bracket at x equals 5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 5, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">b.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345695399\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 1.5 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_223_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 1.5 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">c.<\/span><span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1168345538809\" data-type=\"media\" data-alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 7\/3 is graphed on the number line, with an open parenthesis at x equals negative 7\/3 (written in), and a dark line extending to the left of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 7\/3, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_224_img_new.jpg\" alt=\"This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 7\/3 is graphed on the number line, with an open parenthesis at x equals negative 7\/3 (written in), and a dark line extending to the left of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 7\/3, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 361px;\">5. <span id=\"fs-id1168341955831\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_226_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 361px;\">6. <span id=\"fs-id1168345292799\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_228_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 125px;\">\n<td style=\"width: 33.3333%; height: 125px;\">7. <span id=\"fs-id1168345398216\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17\/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17\/24 is graphed on the number line, with an open bracket at b equals negative 17\/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17\/24 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_230_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17\/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17\/24 is graphed on the number line, with an open bracket at b equals negative 17\/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17\/24 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 125px;\">8. <span id=\"fs-id1168345386567\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: g is less than 23\/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23\/26 is graphed on the number line, with an open parenthesis at g equals 23\/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23\/26, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_232_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: g is less than 23\/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23\/26 is graphed on the number line, with an open parenthesis at g equals 23\/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23\/26, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 125px;\">9. <span data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_234_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 96px;\">\n<td style=\"width: 33.3333%; height: 96px;\">10. <span id=\"fs-id1168345326014\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_236_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 96px;\">11. <span id=\"fs-id1168341955773\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_238_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 96px;\">12. <span id=\"fs-id1168341857412\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_240_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 95px;\">\n<td style=\"width: 33.3333%; height: 95px;\">13. <span id=\"fs-id1168345560404\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_243_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">14. <span id=\"fs-id1168345261323\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_245_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">15. <span id=\"fs-id1168345284656\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_247_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 95px;\">\n<td style=\"width: 33.3333%; height: 95px;\">16. <span id=\"fs-id1168345543291\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_249_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">17. <span id=\"fs-id1168345551424\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_251_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 95px;\">18. <span id=\"fs-id1168345346824\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_253_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 119px;\">\n<td style=\"width: 33.3333%; height: 119px;\">19. <span id=\"fs-id1168345426423\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_255_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 119px;\">20. <span id=\"fs-id1168345637187\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: p is less than 18\/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18\/5 is graphed on the number line, with an open parenthesis at p equals 18\/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18\/5, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_257_img.jpg\" alt=\"At the top of this figure is the solution to the inequality: p is less than 18\/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18\/5 is graphed on the number line, with an open parenthesis at p equals 18\/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18\/5, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 119px;\">21. <span id=\"fs-id1168345448056\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_259_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">22. <span id=\"fs-id1168345432888\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_261_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. <span id=\"fs-id1168345409518\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_263_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">24. <span id=\"fs-id1168345529489\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_265_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. <span id=\"fs-id1168345388259\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_267_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">26. <span id=\"fs-id1168345549932\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_269_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. <span id=\"fs-id1168345250280\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11\/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11\/5 is graphed on the number line, with an open bracket at k equals negative 11\/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11\/5 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_271_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11\/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11\/5 is graphed on the number line, with an open bracket at k equals negative 11\/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11\/5 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 101px;\">\n<td style=\"width: 33.3333%; height: 101px;\">28. <span id=\"fs-id1168345576994\" data-type=\"media\" data-alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_273_img_new.jpg\" alt=\"At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: \u201cNo solution\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 101px;\">29. <span id=\"fs-id1168345500573\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: y is greater than or equal to 10\/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10\/49 is graphed on the number line, with an open bracket at y equals 10\/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10\/49 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_275_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: y is greater than or equal to 10\/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10\/49 is graphed on the number line, with an open bracket at y equals 10\/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10\/49 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 101px;\">30. <span id=\"fs-id1168345640013\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_277_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 94px;\">\n<td style=\"width: 33.3333%; height: 94px;\">31. <span id=\"fs-id1168345675913\" data-type=\"media\" data-alt=\"At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_279_img_new.jpg\" alt=\"At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 94px;\">32. <span id=\"fs-id1168345550085\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_281_img_new.jpg\" alt=\"At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 94px;\">33. <span id=\"fs-id1168345540607\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_283_img_new.jpg\" alt=\"At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 93px;\">\n<td style=\"width: 33.3333%; height: 93px;\">34. <span id=\"fs-id1168345708306\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_285_img_new.jpg\" alt=\"At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">35. <span id=\"fs-id1168345633327\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_287_img_new.jpg\" alt=\"At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">36. <span id=\"fs-id1168345742297\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_289_img_new.jpg\" alt=\"At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 93px;\">\n<td style=\"width: 33.3333%; height: 93px;\">37. <span id=\"fs-id1168345569269\" data-type=\"media\" data-alt=\"At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_07_291_img_new.jpg\" alt=\"At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 33.3333%; height: 93px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-45569dc6632e3f21991bb01a1ceba90b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#32;&#55;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 93px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n","protected":false},"author":125,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["lynn-marecek","maryanne-anthony-smith"],"pb_section_license":""},"chapter-type":[],"contributor":[63,64],"license":[],"class_list":["post-774","chapter","type-chapter","status-publish","hentry","contributor-lynn-marecek","contributor-maryanne-anthony-smith"],"part":272,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/774","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/774\/revisions"}],"predecessor-version":[{"id":775,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/774\/revisions\/775"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/272"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/774\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=774"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=774"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=774"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}