{"id":1009,"date":"2015-11-12T18:35:32","date_gmt":"2015-11-12T18:35:32","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1009"},"modified":"2017-03-31T21:44:44","modified_gmt":"2017-03-31T21:44:44","slug":"key-concepts-glossary-51","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/key-concepts-glossary-51\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul id=\"fs-id1165135332513\"><li>The absolute value function is commonly used to measure distances between points.<\/li>\r\n\t<li>Applied problems, such as ranges of possible values, can also be solved using the absolute value function.<\/li>\r\n\t<li>The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.<\/li>\r\n\t<li>In an absolute value equation, an unknown variable is the input of an absolute value function.<\/li>\r\n\t<li>If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable.<\/li>\r\n\t<li>An absolute value equation may have one solution, two solutions, or no solutions.<\/li>\r\n\t<li>An absolute value inequality is similar to an absolute value equation but takes the form [latex]|A|&lt;B,|A|\\le B,|A|&gt;B,\\text{ or }|A|\\ge B\\\\[\/latex]. It can be solved by determining the boundaries of the solution set and then testing which segments are in the set.<\/li>\r\n\t<li>Absolute value inequalities can also be solved graphically.<\/li>\r\n<\/ul><h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165135191341\" class=\"definition\"><dt>absolute value equation<\/dt><dd id=\"fs-id1165137627032\">an equation of the form [latex]|A|=B[\/latex], with [latex]B\\ge 0[\/latex]; it will have solutions when [latex]A=B[\/latex] or [latex]A=-B[\/latex]<\/dd><\/dl><dl id=\"fs-id1165137560214\" class=\"definition\"><dt>absolute value inequality<\/dt><dd id=\"fs-id1165135173524\">a relationship in the form [latex]|{ A }|&lt;{ B },|{ A }|\\le { B },|{ A }|&gt;{ B },\\text{or }|{ A }|\\ge{ B }[\/latex]<\/dd><\/dl>","rendered":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165135332513\">\n<li>The absolute value function is commonly used to measure distances between points.<\/li>\n<li>Applied problems, such as ranges of possible values, can also be solved using the absolute value function.<\/li>\n<li>The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.<\/li>\n<li>In an absolute value equation, an unknown variable is the input of an absolute value function.<\/li>\n<li>If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable.<\/li>\n<li>An absolute value equation may have one solution, two solutions, or no solutions.<\/li>\n<li>An absolute value inequality is similar to an absolute value equation but takes the form [latex]|A|<B,|A|\\le B,|A|>B,\\text{ or }|A|\\ge B\\\\[\/latex]. It can be solved by determining the boundaries of the solution set and then testing which segments are in the set.<\/li>\n<li>Absolute value inequalities can also be solved graphically.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165135191341\" class=\"definition\">\n<dt>absolute value equation<\/dt>\n<dd id=\"fs-id1165137627032\">an equation of the form [latex]|A|=B[\/latex], with [latex]B\\ge 0[\/latex]; it will have solutions when [latex]A=B[\/latex] or [latex]A=-B[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137560214\" class=\"definition\">\n<dt>absolute value inequality<\/dt>\n<dd id=\"fs-id1165135173524\">a relationship in the form [latex]|{ A }|<{ B },|{ A }|\\le { B },|{ A }|>{ B },\\text{or }|{ A }|\\ge{ B }[\/latex]<\/dd>\n<\/dl>\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-1009\">\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>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/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>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/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":276,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1009","chapter","type-chapter","status-publish","hentry"],"part":992,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1009","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1009\/revisions"}],"predecessor-version":[{"id":2833,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1009\/revisions\/2833"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/992"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1009\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=1009"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1009"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1009"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=1009"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}