{"id":2146,"date":"2021-10-04T16:57:34","date_gmt":"2021-10-04T16:57:34","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2146"},"modified":"2022-03-18T03:39:36","modified_gmt":"2022-03-18T03:39:36","slug":"solving-inequalities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/solving-inequalities\/","title":{"raw":"Solving Inequalities","rendered":"Solving Inequalities"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Solve single-step inequalities<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Solve multi-step inequalities<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Addition and Multiplication Properties of Inequality<\/h2>\r\nSolving inequalities is very similar to solving equations. The difference is that you have to reverse the inequality symbols when you multiply or divide both sides of an inequality by a negative number. We solve inequalities using the <strong>addition property<\/strong> and the <strong>multiplication property<\/strong>.\r\n\r\n<strong>Addition Property<\/strong>\r\n\r\nLet, [latex]a,b,[\/latex] and [latex]c[\/latex] be real numbers.\r\n<p style=\"text-align: center;\">If [latex]a&lt;b[\/latex] then [latex]a+c&lt;b+c[\/latex].<\/p>\r\nThis statement also holds for [latex]a \\leq b, a&gt;b,[\/latex] and [latex]a \\geq b[\/latex].\r\n\r\nFor example,\r\n<p style=\"text-align: center;\">[latex]2&lt;3[\/latex]<\/p>\r\nIf we add 5 to each side of the inequality, we have\r\n<p style=\"text-align: center;\">[latex]2+5&lt;3+5[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]7&lt;8[\/latex]<\/p>\r\nwhich is a true statement. If we add -5 to each side of the inequality,\r\n<p style=\"text-align: center;\">[latex]2+(-5)&lt;3+(-5)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-3&lt;-2[\/latex]<\/p>\r\nwhich is also true. We can add a positive or a negative number to each side of the inequality and the resulting statement is true. Since subtracting a number is the same as adding its negative, we can subtract a number from each side of an inequality and the resulting statement is true.\r\n\r\nRemember when we interchange the expressions on each side of an inequality, the inequality is reversed.\r\n<p style=\"text-align: center;\">[latex]-2&gt;-3[\/latex].<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIllustrate the addition property for inequalities by solving each of the following:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]x-3&lt;5[\/latex]<\/li>\r\n \t<li>[latex]7&gt;2+x[\/latex]<\/li>\r\n \t<li>[latex]x-2 \\leq 4[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"521743\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"521743\"]\r\n\r\nThe addition property for inequalities states that if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.\r\n\r\na) [latex]x-3&lt;5[\/latex]\r\n\r\nAdd 3 to each side.\r\n<p style=\"text-align: center;\">[latex]x-3+3&lt;5+3[\/latex]<\/p>\r\nSimplify.\r\n<p style=\"text-align: center;\">[latex]x&lt;8[\/latex]<\/p>\r\nb) [latex]7&gt;2+x[\/latex]\r\n\r\nSubtract 2 from each side.\r\n<p style=\"text-align: center;\">[latex]7-2&gt;x-2[\/latex]<\/p>\r\nSimplify\r\n<p style=\"text-align: center;\">[latex]5&gt;x[\/latex]<\/p>\r\nReverse the inequality when interchanging the expressions.\r\n<p style=\"text-align: center;\">[latex]x&lt;5[\/latex]<\/p>\r\nc) [latex]x-2 \\leq 4[\/latex]\r\n\r\nAdd 2 to each side.\r\n<p style=\"text-align: center;\">[latex]x-2+2 \\leq 4+2[\/latex]<\/p>\r\nSimplify.\r\n<p style=\"text-align: center;\">[latex]x \\leq 6[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following videos illustrate solving inequalities using the addition property.\r\n\r\nhttps:\/\/youtu.be\/1Z22Xh66VFM\r\n\r\nhttps:\/\/youtu.be\/RBonYKvTCLU\r\n\r\nSuppose in the example [latex]2&lt;3[\/latex] we multiplied by [latex]5[\/latex]. Since [latex]2 \\cdot 5=10[\/latex] and [latex]3 \\cdot 5=15[\/latex], and [latex]10&lt;15[\/latex], the relationship between the products is the same. On the other hand, if we multiplied by [latex]-5[\/latex], we would have [latex]2(-5)=-10[\/latex] and [latex]3(-5)=-15[\/latex], and [latex]-10&gt; -15[\/latex]. The inequality changes from less than [latex](&lt;)[\/latex] to greater than [latex](&gt;)[\/latex]. When we multiply both sides of an inequality by a negative, the inequality is reversed.\r\n\r\n<strong>Multiplication Property<\/strong>\r\n\r\nLet, [latex]a,b,[\/latex] and [latex]c[\/latex] be real numbers.\r\n<p style=\"text-align: center;\">If [latex]a&lt;b[\/latex] and [latex]c&gt;0[\/latex] then [latex]a \\ cdot c&lt;b \\cdot c[\/latex].<\/p>\r\n<p style=\"text-align: center;\">If [latex]a&lt;b[\/latex] and [latex]c&lt;0[\/latex] then [latex]a \\ cdot c&gt;b \\cdot c[\/latex].<\/p>\r\nThis statement also holds for [latex]a \\leq b, a&gt;b,[\/latex] and [latex]a \\geq b[\/latex].\r\n\r\nSince division is the same as multiplying by the reciprocal, when we divide each side of an inequality by a positive number, the inequality stays the same. But if we divide each side of an inequality by a negative number, the inequality is reversed.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIllustrate the multiplication property for inequalities by solving each of the following:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]3x \\geq 15[\/latex]<\/li>\r\n \t<li>[latex]2x-1 &lt; 9[\/latex]<\/li>\r\n \t<li>[latex]3-4x &gt; 15[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"387013\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"387013\"]\r\n\r\na)\r\n<p style=\"text-align: center;\">[latex]3x \\geq 15[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{3} (3x) \\geq \\frac{1}{3} (15)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x \\geq 5[\/latex]<\/p>\r\nb)\r\n<p style=\"text-align: center;\">[latex]2x-1&lt;9[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]2x-1+1&lt;9+1[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]2x&lt;10[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{2} (2x)&lt; \\frac{1}{2} (10)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x&lt;5[\/latex]<\/p>\r\nc)\r\n<p style=\"text-align: center;\">[latex]3-4x &gt; 15[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]3-4x - 3 &gt; 15 - 3[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-4x &gt; 12[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]- \\frac{1}{4} (-4x) &lt; - \\frac{1}{4} (12)[\/latex]<\/p>\r\n*We reverse the inequality when multiplying by a negative.\r\n<p style=\"text-align: center;\">[latex]x&lt;-3[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]2917[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>\u00a0Solve Multi-Step Inequalities<\/h2>\r\nAs the previous examples have shown, we can perform the same operations on both sides of an inequality just as we do with equations. To isolate the variable and solve, we combine like terms and perform operations with the multiplication and addition properties.\r\n<div class=\"textbox exercises\" style=\"text-align: left;\">\r\n<h3>Example<\/h3>\r\nSolve the inequality: [latex]13 - 7x\\ge 10x - 4[\/latex].\r\n\r\n[reveal-answer q=\"532189\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"532189\"]\r\n\r\nSolving this inequality is similar to solving an equation up until the last step.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{rr}13 - 7x\\ge 10x - 4\\hfill &amp; \\\\ 13 - 17x\\ge -4\\hfill &amp; \\text{Move variable terms to one side of the inequality}.\\hfill&amp;\\quad \\\\-17x\\ge -17\\hfill&amp;\\text{Isolate the variable term}.\\hfill&amp;\\quad \\\\x\\le 1\\hfill &amp; \\text{Dividing both sides by -17 reverses the inequality}.\\hfill \\end{array}[\/latex]<\/div>\r\nThe solution set is given by the interval [latex]\\left(-\\infty ,1\\right][\/latex], or all real numbers less than and including 1.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]143594[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Solve single-step inequalities<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Solve multi-step inequalities<\/li>\n<\/ul>\n<\/div>\n<h2>Addition and Multiplication Properties of Inequality<\/h2>\n<p>Solving inequalities is very similar to solving equations. The difference is that you have to reverse the inequality symbols when you multiply or divide both sides of an inequality by a negative number. We solve inequalities using the <strong>addition property<\/strong> and the <strong>multiplication property<\/strong>.<\/p>\n<p><strong>Addition Property<\/strong><\/p>\n<p>Let, [latex]a,b,[\/latex] and [latex]c[\/latex] be real numbers.<\/p>\n<p style=\"text-align: center;\">If [latex]a<b[\/latex] then [latex]a+c<b+c[\/latex].<\/p>\n<p>This statement also holds for [latex]a \\leq b, a>b,[\/latex] and [latex]a \\geq b[\/latex].<\/p>\n<p>For example,<\/p>\n<p style=\"text-align: center;\">[latex]2<3[\/latex]<\/p>\n<p>If we add 5 to each side of the inequality, we have<\/p>\n<p style=\"text-align: center;\">[latex]2+5<3+5[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]7<8[\/latex]<\/p>\n<p>which is a true statement. If we add -5 to each side of the inequality,<\/p>\n<p style=\"text-align: center;\">[latex]2+(-5)<3+(-5)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-3<-2[\/latex]<\/p>\n<p>which is also true. We can add a positive or a negative number to each side of the inequality and the resulting statement is true. Since subtracting a number is the same as adding its negative, we can subtract a number from each side of an inequality and the resulting statement is true.<\/p>\n<p>Remember when we interchange the expressions on each side of an inequality, the inequality is reversed.<\/p>\n<p style=\"text-align: center;\">[latex]-2>-3[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Illustrate the addition property for inequalities by solving each of the following:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]x-3<5[\/latex]<\/li>\n<li>[latex]7>2+x[\/latex]<\/li>\n<li>[latex]x-2 \\leq 4[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q521743\">Show Answer<\/span><\/p>\n<div id=\"q521743\" class=\"hidden-answer\" style=\"display: none\">\n<p>The addition property for inequalities states that if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.<\/p>\n<p>a) [latex]x-3<5[\/latex]\n\nAdd 3 to each side.\n\n\n<p style=\"text-align: center;\">[latex]x-3+3<5+3[\/latex]<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center;\">[latex]x<8[\/latex]<\/p>\n<p>b) [latex]7>2+x[\/latex]<\/p>\n<p>Subtract 2 from each side.<\/p>\n<p style=\"text-align: center;\">[latex]7-2>x-2[\/latex]<\/p>\n<p>Simplify<\/p>\n<p style=\"text-align: center;\">[latex]5>x[\/latex]<\/p>\n<p>Reverse the inequality when interchanging the expressions.<\/p>\n<p style=\"text-align: center;\">[latex]x<5[\/latex]<\/p>\n<p>c) [latex]x-2 \\leq 4[\/latex]<\/p>\n<p>Add 2 to each side.<\/p>\n<p style=\"text-align: center;\">[latex]x-2+2 \\leq 4+2[\/latex]<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center;\">[latex]x \\leq 6[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following videos illustrate solving inequalities using the addition property.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Solving One Step Inequalities by Adding and Subtracting (Variable Left Side)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/1Z22Xh66VFM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Solving One Step Inequalities by Adding and Subtracting (Variable Right Side)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/RBonYKvTCLU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Suppose in the example [latex]2<3[\/latex] we multiplied by [latex]5[\/latex]. Since [latex]2 \\cdot 5=10[\/latex] and [latex]3 \\cdot 5=15[\/latex], and [latex]10<15[\/latex], the relationship between the products is the same. On the other hand, if we multiplied by [latex]-5[\/latex], we would have [latex]2(-5)=-10[\/latex] and [latex]3(-5)=-15[\/latex], and [latex]-10> -15[\/latex]. The inequality changes from less than [latex](<)[\/latex] to greater than [latex](>)[\/latex]. When we multiply both sides of an inequality by a negative, the inequality is reversed.<\/p>\n<p><strong>Multiplication Property<\/strong><\/p>\n<p>Let, [latex]a,b,[\/latex] and [latex]c[\/latex] be real numbers.<\/p>\n<p style=\"text-align: center;\">If [latex]a<b[\/latex] and [latex]c>0[\/latex] then [latex]a \\ cdot c<b \\cdot c[\/latex].<\/p>\n<p style=\"text-align: center;\">If [latex]a<b[\/latex] and [latex]c<0[\/latex] then [latex]a \\ cdot c>b \\cdot c[\/latex].<\/p>\n<p>This statement also holds for [latex]a \\leq b, a>b,[\/latex] and [latex]a \\geq b[\/latex].<\/p>\n<p>Since division is the same as multiplying by the reciprocal, when we divide each side of an inequality by a positive number, the inequality stays the same. But if we divide each side of an inequality by a negative number, the inequality is reversed.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Illustrate the multiplication property for inequalities by solving each of the following:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]3x \\geq 15[\/latex]<\/li>\n<li>[latex]2x-1 < 9[\/latex]<\/li>\n<li>[latex]3-4x > 15[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q387013\">Show Answer<\/span><\/p>\n<div id=\"q387013\" class=\"hidden-answer\" style=\"display: none\">\n<p>a)<\/p>\n<p style=\"text-align: center;\">[latex]3x \\geq 15[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{3} (3x) \\geq \\frac{1}{3} (15)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x \\geq 5[\/latex]<\/p>\n<p>b)<\/p>\n<p style=\"text-align: center;\">[latex]2x-1<9[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]2x-1+1<9+1[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]2x<10[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{2} (2x)< \\frac{1}{2} (10)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x<5[\/latex]<\/p>\n<p>c)<\/p>\n<p style=\"text-align: center;\">[latex]3-4x > 15[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]3-4x - 3 > 15 - 3[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-4x > 12[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]- \\frac{1}{4} (-4x) < - \\frac{1}{4} (12)[\/latex]<\/p>\n<p>*We reverse the inequality when multiplying by a negative.<\/p>\n<p style=\"text-align: center;\">[latex]x<-3[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm2917\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=2917&theme=oea&iframe_resize_id=ohm2917&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>\u00a0Solve Multi-Step Inequalities<\/h2>\n<p>As the previous examples have shown, we can perform the same operations on both sides of an inequality just as we do with equations. To isolate the variable and solve, we combine like terms and perform operations with the multiplication and addition properties.<\/p>\n<div class=\"textbox exercises\" style=\"text-align: left;\">\n<h3>Example<\/h3>\n<p>Solve the inequality: [latex]13 - 7x\\ge 10x - 4[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q532189\">Show Solution<\/span><\/p>\n<div id=\"q532189\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solving this inequality is similar to solving an equation up until the last step.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{rr}13 - 7x\\ge 10x - 4\\hfill & \\\\ 13 - 17x\\ge -4\\hfill & \\text{Move variable terms to one side of the inequality}.\\hfill&\\quad \\\\-17x\\ge -17\\hfill&\\text{Isolate the variable term}.\\hfill&\\quad \\\\x\\le 1\\hfill & \\text{Dividing both sides by -17 reverses the inequality}.\\hfill \\end{array}[\/latex]<\/div>\n<p>The solution set is given by the interval [latex]\\left(-\\infty ,1\\right][\/latex], or all real numbers less than and including 1.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143594\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143594&theme=oea&iframe_resize_id=ohm143594&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2146\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Left Side). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/1Z22Xh66VFM\">https:\/\/youtu.be\/1Z22Xh66VFM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Right Side). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/RBonYKvTCLU\">https:\/\/youtu.be\/RBonYKvTCLU<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 2917, 143594. <strong>Authored by<\/strong>: Lippman, D; Hughes Martin, C. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Left Side)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/1Z22Xh66VFM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Right Side)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/RBonYKvTCLU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 2917, 143594\",\"author\":\"Lippman, D; 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