{"id":1182,"date":"2023-07-23T18:51:26","date_gmt":"2023-07-23T18:51:26","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/?post_type=chapter&#038;p=1182"},"modified":"2023-08-10T23:44:30","modified_gmt":"2023-08-10T23:44:30","slug":"summary-polynomial-and-rational-inequalities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-polynomial-and-rational-inequalities\/","title":{"raw":"Summary: Polynomial and Rational Inequalities","rendered":"Summary: Polynomial and Rational Inequalities"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li>Boundary points are 1) solutions of the polynomial or rational equation AND 2) restrictions of the rational equation of the given inequality when it is available.<\/li>\r\n \t<li>When we plot the boundary points, solutions can be either open circles (if [latex]&lt;[\/latex] or [latex]&gt;[\/latex]) or closed circles (if [latex]\\leq[\/latex] or [latex]\\geq[\/latex]) based on the inequality sign of the given inequality while\u00a0restrictions are always open circles.<\/li>\r\n \t<li>Any number in each interval could be a test value for the interval.<\/li>\r\n \t<li>If a test value makes the given inequality true, the interval is a solution of the inequality.<\/li>\r\n<\/ul>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Boundary points are 1) solutions of the polynomial or rational equation AND 2) restrictions of the rational equation of the given inequality when it is available.<\/li>\n<li>When we plot the boundary points, solutions can be either open circles (if [latex]<[\/latex] or [latex]>[\/latex]) or closed circles (if [latex]\\leq[\/latex] or [latex]\\geq[\/latex]) based on the inequality sign of the given inequality while\u00a0restrictions are always open circles.<\/li>\n<li>Any number in each interval could be a test value for the interval.<\/li>\n<li>If a test value makes the given inequality true, the interval is a solution of the inequality.<\/li>\n<\/ul>\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-1182\">\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>Summary: Polynomial and Rational Inequalities. <strong>Authored by<\/strong>: Michelle Eunhee Chung. <strong>Provided by<\/strong>: Georgia State University . <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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":705214,"menu_order":38,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Summary: Polynomial and Rational Inequalities\",\"author\":\"Michelle Eunhee 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