{"id":2155,"date":"2021-10-04T19:01:05","date_gmt":"2021-10-04T19:01:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2155"},"modified":"2022-03-18T02:34:20","modified_gmt":"2022-03-18T02:34:20","slug":"summary-review-9","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-9\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li>Inequalities are solved using the following properties.<\/li>\r\n<\/ul>\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\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<ul>\r\n \t<li>We solve an inequality by isolating the variable, just like when solving an equation, but remember to reverse the inequality when multiplying or dividing by a negative number.<\/li>\r\n \t<li>A compound inequality involving <em>or<\/em> has a solution set made up of all real numbers which satisfy the first inequality or the second inequality, or both.<\/li>\r\n \t<li>The solution to an <em>and<\/em> compound inequality is all the solutions that the two inequalities have in common. This is where the two graphs overlap.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>compound inequality:<\/strong> two inequalities joined with the word <em>and<\/em> or the word <em>or<\/em>.\r\n\r\n&nbsp;","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Inequalities are solved using the following properties.<\/li>\n<\/ul>\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><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<ul>\n<li>We solve an inequality by isolating the variable, just like when solving an equation, but remember to reverse the inequality when multiplying or dividing by a negative number.<\/li>\n<li>A compound inequality involving <em>or<\/em> has a solution set made up of all real numbers which satisfy the first inequality or the second inequality, or both.<\/li>\n<li>The solution to an <em>and<\/em> compound inequality is all the solutions that the two inequalities have in common. This is where the two graphs overlap.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>compound inequality:<\/strong> two inequalities joined with the word <em>and<\/em> or the word <em>or<\/em>.<\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2155\">\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><\/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":5,"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\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2155","chapter","type-chapter","status-publish","hentry"],"part":276,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2155\/revisions"}],"predecessor-version":[{"id":3824,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2155\/revisions\/3824"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/276"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2155\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2155"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2155"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2155"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}