{"id":9023,"date":"2017-05-01T15:08:24","date_gmt":"2017-05-01T15:08:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9023"},"modified":"2020-05-01T23:59:08","modified_gmt":"2020-05-01T23:59:08","slug":"summary-solve-equations-using-the-division-and-multiplication-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/chapter\/summary-solve-equations-using-the-division-and-multiplication-properties-of-equality\/","title":{"raw":"Summary: Solving Equations Using the Division and Multiplication Properties of Equality","rendered":"Summary: Solving Equations Using the Division and Multiplication Properties of Equality"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-141\">\r\n \t<li><strong>Division and Multiplication Properties of Equality<\/strong>\r\n<ul id=\"eip-id1170323851320\">\r\n \t<li><strong>Division Property of Equality:<\/strong> For all real numbers <em>a, b, c,<\/em> and [latex]c\\ne 0[\/latex] , if [latex]a=b[\/latex] , then [latex]ac=bc[\/latex] .<\/li>\r\n \t<li><strong>Multiplication Property of Equality:<\/strong> For all real numbers <em>a, b, c,<\/em> if [latex]a=b[\/latex] , then [latex]ac=bc[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<ul id=\"eip-578\">\r\n \t<li><strong>Solve an equation with variables and constants on both sides<\/strong>\r\n<ol id=\"eip-id1170322988380\" class=\"stepwise\">\r\n \t<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\r\n \t<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Make the coefficient of the variable[latex]1[\/latex], using the Multiplication or Division Property of Equality.<\/li>\r\n \t<li>Check the solution by substituting into the original equation.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>General strategy for solving linear equations<\/strong>\r\n<ol id=\"eip-id1170324010914\" class=\"stepwise\">\r\n \t<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\r\n \t<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Make the coefficient of the variable term equal to [latex]1[\/latex]. Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\r\n \t<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h1 style=\"text-align: center\"><span style=\"color: #ff0000\"><strong>STOP!<\/strong><\/span><\/h1>\r\n<h1 style=\"text-align: center\"><span style=\"color: #ff0000\"><strong>You have now completed this section.\u00a0 Go back to your course menu and complete the Practice Problems for this section<\/strong><\/span><\/h1>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-141\">\n<li><strong>Division and Multiplication Properties of Equality<\/strong>\n<ul id=\"eip-id1170323851320\">\n<li><strong>Division Property of Equality:<\/strong> For all real numbers <em>a, b, c,<\/em> and [latex]c\\ne 0[\/latex] , if [latex]a=b[\/latex] , then [latex]ac=bc[\/latex] .<\/li>\n<li><strong>Multiplication Property of Equality:<\/strong> For all real numbers <em>a, b, c,<\/em> if [latex]a=b[\/latex] , then [latex]ac=bc[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul id=\"eip-578\">\n<li><strong>Solve an equation with variables and constants on both sides<\/strong>\n<ol id=\"eip-id1170322988380\" class=\"stepwise\">\n<li>Choose one side to be the variable side and then the other will be the constant side.<\/li>\n<li>Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect the constants to the other side, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable[latex]1[\/latex], using the Multiplication or Division Property of Equality.<\/li>\n<li>Check the solution by substituting into the original equation.<\/li>\n<\/ol>\n<\/li>\n<li><strong>General strategy for solving linear equations<\/strong>\n<ol id=\"eip-id1170324010914\" class=\"stepwise\">\n<li>Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.<\/li>\n<li>Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable term equal to [latex]1[\/latex]. Use the Multiplication or Division Property of Equality. State the solution to the equation.<\/li>\n<li>Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 style=\"text-align: center\"><span style=\"color: #ff0000\"><strong>STOP!<\/strong><\/span><\/h1>\n<h1 style=\"text-align: center\"><span style=\"color: #ff0000\"><strong>You have now completed this section.\u00a0 Go back to your course menu and complete the Practice Problems for this section<\/strong><\/span><\/h1>\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-9023\">\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":12,"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":"45c7a3a4-572e-4842-bcd3-f17fc94bb71d","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9023","chapter","type-chapter","status-publish","hentry"],"part":7476,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9023","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9023\/revisions"}],"predecessor-version":[{"id":16017,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9023\/revisions\/16017"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/parts\/7476"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9023\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/media?parent=9023"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9023"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/contributor?post=9023"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/license?post=9023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}