{"id":1861,"date":"2021-09-13T18:38:32","date_gmt":"2021-09-13T18:38:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1861"},"modified":"2022-02-07T18:46:58","modified_gmt":"2022-02-07T18:46:58","slug":"summary-review-7","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-7\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A proportion can be solved by multiplying both sides by the lowest common denominator (LCD).<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">To solve a proportion by finding cross products:\r\n<ul>\r\n \t<li aria-level=\"1\">If [latex]\\frac{a}{b}=\\frac{c}{d}[\/latex], where [latex]b \\neq 0, d \\neq 0[\/latex], then [latex]a \\cdot d = b \\cdot c[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Square root property:<\/strong> If [latex]x^2=k[\/latex], then [latex]x = \\pm \\sqrt{k}[\/latex]\r\n<ul>\r\n \t<li>If [latex]k&gt;0[\/latex] the equation has two solutions<\/li>\r\n \t<li>If [latex]k=0[\/latex] the equation has one solution<\/li>\r\n \t<li>If [latex]k&lt;0[\/latex] the equation has no solution<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>We can remove a radical from an equation using the following two properties:\r\n<ul>\r\n \t<li>if [latex]a=b[\/latex] then [latex]a^2 = b^2[\/latex]<\/li>\r\n \t<li>for [latex]x \\geq 0, (\\sqrt{x})^2=x[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">To solve a radical equation:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">Isolate the radical expression<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">Square both sides of the equation<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">Once the radical is removed, solve for the unknown<\/li>\r\n \t<li aria-level=\"2\">Check your solution<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>extraneous solutions:<\/strong>\u00a0solutions that do not create a true statement when substituted back into the original equation\r\n\r\n<strong>proportion:<\/strong> a equation of the form [latex]\\frac{a}{b}=\\frac{c}{d}[\/latex], where [latex]b \\neq 0, d \\neq 0[\/latex]\r\n\r\n<strong>quadratic equation:<\/strong> can be written [latex]ax^2+bx+c=0, a \\neq 0, b \\ \\mathrm{and} \\ c[\/latex] are constants\r\n\r\n<strong>radical equation:<\/strong> equation containing a radical such as a square root","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A proportion can be solved by multiplying both sides by the lowest common denominator (LCD).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">To solve a proportion by finding cross products:\n<ul>\n<li aria-level=\"1\">If [latex]\\frac{a}{b}=\\frac{c}{d}[\/latex], where [latex]b \\neq 0, d \\neq 0[\/latex], then [latex]a \\cdot d = b \\cdot c[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li><strong>Square root property:<\/strong> If [latex]x^2=k[\/latex], then [latex]x = \\pm \\sqrt{k}[\/latex]\n<ul>\n<li>If [latex]k>0[\/latex] the equation has two solutions<\/li>\n<li>If [latex]k=0[\/latex] the equation has one solution<\/li>\n<li>If [latex]k<0[\/latex] the equation has no solution<\/li>\n<\/ul>\n<\/li>\n<li>We can remove a radical from an equation using the following two properties:\n<ul>\n<li>if [latex]a=b[\/latex] then [latex]a^2 = b^2[\/latex]<\/li>\n<li>for [latex]x \\geq 0, (\\sqrt{x})^2=x[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">To solve a radical equation:\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\">Isolate the radical expression<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">Square both sides of the equation<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">Once the radical is removed, solve for the unknown<\/li>\n<li aria-level=\"2\">Check your solution<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>extraneous solutions:<\/strong>\u00a0solutions that do not create a true statement when substituted back into the original equation<\/p>\n<p><strong>proportion:<\/strong> a equation of the form [latex]\\frac{a}{b}=\\frac{c}{d}[\/latex], where [latex]b \\neq 0, d \\neq 0[\/latex]<\/p>\n<p><strong>quadratic equation:<\/strong> can be written [latex]ax^2+bx+c=0, a \\neq 0, b \\ \\mathrm{and} \\ c[\/latex] are constants<\/p>\n<p><strong>radical equation:<\/strong> equation containing a radical such as a square root<\/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-1861\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\">https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/a>. <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>: Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/li><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay, et al. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/college-algebra\/pages\/1-introduction-to-prerequisites\">https:\/\/openstax.org\/books\/college-algebra\/pages\/1-introduction-to-prerequisites<\/a>. <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>: Access for free at https:\/\/openstax.org\/books\/college-algebra\/pages\/1-introduction-to-prerequisites<\/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":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay, et al\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/college-algebra\/pages\/1-introduction-to-prerequisites\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/college-algebra\/pages\/1-introduction-to-prerequisites\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1861","chapter","type-chapter","status-publish","hentry"],"part":262,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1861","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":6,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1861\/revisions"}],"predecessor-version":[{"id":3705,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1861\/revisions\/3705"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/262"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1861\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1861"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1861"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1861"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}