{"id":10375,"date":"2017-05-26T18:51:18","date_gmt":"2017-05-26T18:51:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10375"},"modified":"2024-04-30T16:35:15","modified_gmt":"2024-04-30T16:35:15","slug":"summary-solving-equations-with-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-solving-equations-with-decimals\/","title":{"raw":"Summary: Solving Equations Containing Decimals","rendered":"Summary: Solving Equations Containing Decimals"},"content":{"raw":"<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<ul id=\"eip-81\">\r\n \t<li><strong>Determine whether a number is a solution to an equation.<\/strong>\r\n<ul id=\"eip-id1170326284956\">\r\n \t<li>Substitute the number for the variable in the equation.<\/li>\r\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Determine whether the resulting equation is true. If so, the number is a solution. If not, the number is not a solution.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Properties of Equality<\/strong><\/li>\r\n<\/ul>\r\n<table id=\"eip-778\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><strong>Subtraction Property of Equality<\/strong><\/td>\r\n<td><strong>Addition Property of Equality<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,\r\n\r\n[latex]\\begin{array}{cccc}\\text{If}&amp; \\hfill a&amp; =&amp; b\\hfill \\\\ \\text{then}&amp; \\hfill a-c&amp; =&amp; b-c\\hfill \\end{array}[\/latex]<\/td>\r\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,\r\n\r\n[latex]\\begin{array}{cccc}\\text{If}&amp; \\hfill a&amp; =&amp; b\\hfill \\\\ \\text{then}&amp; \\hfill a+c&amp; =&amp; b+c\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Division of Property of Equality<\/strong><\/td>\r\n<td><strong>Multiplication Property of Equality<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c\\ne 0[\/latex] ,\r\n\r\n[latex]\\begin{array}{cccc}\\text{If}&amp; \\hfill a&amp; =&amp; b\\hfill \\\\ \\text{then}&amp; \\hfill \\frac{a}{c}&amp; =&amp; \\frac{b}{c}\\hfill \\end{array}[\/latex]<\/td>\r\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,\r\n\r\n[latex]\\begin{array}{cccc}\\text{If}&amp; \\hfill a&amp; =&amp; b\\hfill \\\\ \\text{then}&amp; \\hfill a\\cdot c&amp; =&amp; b\\cdot c\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"eip-81\">\n<li><strong>Determine whether a number is a solution to an equation.<\/strong>\n<ul id=\"eip-id1170326284956\">\n<li>Substitute the number for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting equation is true. If so, the number is a solution. If not, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Properties of Equality<\/strong><\/li>\n<\/ul>\n<table id=\"eip-778\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Subtraction Property of Equality<\/strong><\/td>\n<td><strong>Addition Property of Equality<\/strong><\/td>\n<\/tr>\n<tr>\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,<\/p>\n<p>[latex]\\begin{array}{cccc}\\text{If}& \\hfill a& =& b\\hfill \\\\ \\text{then}& \\hfill a-c& =& b-c\\hfill \\end{array}[\/latex]<\/td>\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,<\/p>\n<p>[latex]\\begin{array}{cccc}\\text{If}& \\hfill a& =& b\\hfill \\\\ \\text{then}& \\hfill a+c& =& b+c\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>Division of Property of Equality<\/strong><\/td>\n<td><strong>Multiplication Property of Equality<\/strong><\/td>\n<\/tr>\n<tr>\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c\\ne 0[\/latex] ,<\/p>\n<p>[latex]\\begin{array}{cccc}\\text{If}& \\hfill a& =& b\\hfill \\\\ \\text{then}& \\hfill \\frac{a}{c}& =& \\frac{b}{c}\\hfill \\end{array}[\/latex]<\/td>\n<td>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,<\/p>\n<p>[latex]\\begin{array}{cccc}\\text{If}& \\hfill a& =& b\\hfill \\\\ \\text{then}& \\hfill a\\cdot c& =& b\\cdot c\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-10375\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":17533,"menu_order":23,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"0bb2ce08501f445ea2b4a13f4dd7c625","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10375","chapter","type-chapter","status-publish","hentry"],"part":6986,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10375\/revisions"}],"predecessor-version":[{"id":20379,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10375\/revisions\/20379"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/6986"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10375\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10375"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10375"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10375"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=10375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}