{"id":9413,"date":"2017-05-02T22:20:51","date_gmt":"2017-05-02T22:20:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9413"},"modified":"2020-01-09T00:21:58","modified_gmt":"2020-01-09T00:21:58","slug":"summary-solving-one-step-equations-using-the-subtraction-and-addition-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/summary-solving-one-step-equations-using-the-subtraction-and-addition-properties-of-equality\/","title":{"raw":"Summary: Solving one-step Equations Using Whole Numbers","rendered":"Summary: Solving one-step Equations Using Whole Numbers"},"content":{"raw":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,\r\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\r\n<h2>Key Concepts<\/h2>\r\n<ul id=\"fs-id2692025\">\r\n \t<li><strong>Determine whether a number is a solution to an equation.<\/strong>\r\n<ol id=\"eip-id1168262511558\" class=\"stepwise\">\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 it is true, the number is a solution.<\/li>\r\n<\/ol>\r\nIf it is not true, the number is not a solution.<\/li>\r\n \t<li><strong>Subtraction Property of Equality<\/strong>\r\n<ul id=\"eip-id1168263809757\">\r\n \t<li>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,\r\n<table id=\"eip-466\" class=\"unnumbered\" summary=\"if a = b then a - c = b - c\">\r\n<tbody>\r\n<tr>\r\n<td>if<\/td>\r\n<td>[latex]a=b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>then<\/td>\r\n<td>[latex]a-b=b-c[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Solve an equation using the Subtraction Property of Equality.<\/strong>\r\n<ol id=\"eip-id1170196360074\" class=\"stepwise\">\r\n \t<li>Use the Subtraction Property of Equality to isolate the variable.<\/li>\r\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Check the solution.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Addition Property of Equality<\/strong>\r\n<ul id=\"eip-id1170195252335\">\r\n \t<li>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,\r\n<table id=\"eip-id1170195252351\" class=\"unnumbered\" summary=\"if a = b then a + c = b + c\">\r\n<tbody>\r\n<tr>\r\n<td>if<\/td>\r\n<td>[latex]a=b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>then<\/td>\r\n<td>[latex]a+b=b+c[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Solve an equation using the Addition Property of Equality.<\/strong>\r\n<ol id=\"eip-id1170195169760\" class=\"stepwise\">\r\n \t<li>Use the Addition Property of Equality to isolate the variable.<\/li>\r\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Check the solution.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id2261028\" class=\"definition\">\r\n \t<dt><strong>solution of an equation<\/strong><\/dt>\r\n \t<dd id=\"fs-id2819300\">A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation.<\/dd>\r\n<\/dl>\r\n&nbsp;","rendered":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,<br \/>\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\n<h2>Key Concepts<\/h2>\n<ul id=\"fs-id2692025\">\n<li><strong>Determine whether a number is a solution to an equation.<\/strong>\n<ol id=\"eip-id1168262511558\" class=\"stepwise\">\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 it is true, the number is a solution.<\/li>\n<\/ol>\n<p>If it is not true, the number is not a solution.<\/li>\n<li><strong>Subtraction Property of Equality<\/strong>\n<ul id=\"eip-id1168263809757\">\n<li>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,<br \/>\n<table id=\"eip-466\" class=\"unnumbered\" summary=\"if a = b then a - c = b - c\">\n<tbody>\n<tr>\n<td>if<\/td>\n<td>[latex]a=b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>then<\/td>\n<td>[latex]a-b=b-c[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Solve an equation using the Subtraction Property of Equality.<\/strong>\n<ol id=\"eip-id1170196360074\" class=\"stepwise\">\n<li>Use the Subtraction Property of Equality to isolate the variable.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Check the solution.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Addition Property of Equality<\/strong>\n<ul id=\"eip-id1170195252335\">\n<li>For any numbers [latex]a[\/latex] , [latex]b[\/latex] , and [latex]c[\/latex] ,<br \/>\n<table id=\"eip-id1170195252351\" class=\"unnumbered\" summary=\"if a = b then a + c = b + c\">\n<tbody>\n<tr>\n<td>if<\/td>\n<td>[latex]a=b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>then<\/td>\n<td>[latex]a+b=b+c[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Solve an equation using the Addition Property of Equality.<\/strong>\n<ol id=\"eip-id1170195169760\" class=\"stepwise\">\n<li>Use the Addition Property of Equality to isolate the variable.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Check the solution.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id2261028\" class=\"definition\">\n<dt><strong>solution of an equation<\/strong><\/dt>\n<dd id=\"fs-id2819300\">A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation.<\/dd>\n<\/dl>\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-9413\">\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":5,"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":"f58f6912-2bb6-4d65-86c7-a294ef6a636a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9413","chapter","type-chapter","status-publish","hentry"],"part":16105,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9413\/revisions"}],"predecessor-version":[{"id":16076,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9413\/revisions\/16076"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/16105"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9413\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=9413"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9413"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=9413"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=9413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}