{"id":9367,"date":"2017-05-02T21:53:05","date_gmt":"2017-05-02T21:53:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9367"},"modified":"2017-12-18T19:31:52","modified_gmt":"2017-12-18T19:31:52","slug":"summary-solving-one-step-equations-using-integers-the-division-property-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-solving-one-step-equations-using-integers-the-division-property-of-equality\/","title":{"raw":"Summary: Solving one step Equations Using Integers","rendered":"Summary: Solving one step Equations Using Integers"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"fs-id2993295\">\r\n \t<li><strong>How to determine whether a number is a solution to an equation.<\/strong>\r\n<ul id=\"eip-id1168468279104\">\r\n \t<li>Step 1. Substitute the number for the variable in the equation.<\/li>\r\n \t<li>Step 2. Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Step 3. Determine whether the resulting equation is true.\r\n<ul id=\"eip-id1168468279113\">\r\n \t<li>If it is true, the number is a solution.<\/li>\r\n \t<li>If it is not true, the number is not a solution.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Properties of Equalities<\/strong>\r\n<table id=\"eip-id1168468439592\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column is labeled subtraction property of equality. The second column is labeled addition property of equality. In the row under the first column, subtraction property of equality, it states for any numbers, a, b, and c, if a equals b, then a minus c equals b minus c. In the row under the second column, addition property of equality, it states for any numbers a, b, and c, if a equals b, then a plus c\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Subtraction Property of Equality<\/th>\r\n<th>Addition Property of Equality<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>For any numbers [latex]a,b,c[\/latex],\r\n\r\nif [latex]a=b[\/latex] then [latex]a-c=b-c[\/latex].<\/td>\r\n<td>For any numbers [latex]a,b,c[\/latex],\r\n\r\nif [latex]a=b[\/latex] then [latex]a+c=b+c[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li><strong>Division Property of Equality<\/strong>\r\n<ul id=\"eip-id1168469635815\">\r\n \t<li>For any numbers [latex]a,b,c[\/latex], and [latex]c\\ne 0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p style=\"padding-left: 120px;\">If [latex]a=b[\/latex] , then [latex]\\Large{\\frac{a}{c}=\\frac{b}{c}}[\/latex].<\/p>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"fs-id2993295\">\n<li><strong>How to determine whether a number is a solution to an equation.<\/strong>\n<ul id=\"eip-id1168468279104\">\n<li>Step 1. Substitute the number for the variable in the equation.<\/li>\n<li>Step 2. Simplify the expressions on both sides of the equation.<\/li>\n<li>Step 3. Determine whether the resulting equation is true.\n<ul id=\"eip-id1168468279113\">\n<li>If it is true, the number is a solution.<\/li>\n<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Properties of Equalities<\/strong><br \/>\n<table id=\"eip-id1168468439592\" class=\"unnumbered\" summary=\"This is a table with two columns. The first column is labeled subtraction property of equality. The second column is labeled addition property of equality. In the row under the first column, subtraction property of equality, it states for any numbers, a, b, and c, if a equals b, then a minus c equals b minus c. In the row under the second column, addition property of equality, it states for any numbers a, b, and c, if a equals b, then a plus c\">\n<thead>\n<tr valign=\"top\">\n<th>Subtraction Property of Equality<\/th>\n<th>Addition Property of Equality<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>For any numbers [latex]a,b,c[\/latex],<\/p>\n<p>if [latex]a=b[\/latex] then [latex]a-c=b-c[\/latex].<\/td>\n<td>For any numbers [latex]a,b,c[\/latex],<\/p>\n<p>if [latex]a=b[\/latex] then [latex]a+c=b+c[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li><strong>Division Property of Equality<\/strong>\n<ul id=\"eip-id1168469635815\">\n<li>For any numbers [latex]a,b,c[\/latex], and [latex]c\\ne 0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"padding-left: 120px;\">If [latex]a=b[\/latex] , then [latex]\\Large{\\frac{a}{c}=\\frac{b}{c}}[\/latex].<\/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-9367\">\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":27,"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":"99af8f2d-2cd4-45d9-8db7-232d3918d8d4","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9367","chapter","type-chapter","status-publish","hentry"],"part":6350,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9367\/revisions"}],"predecessor-version":[{"id":15584,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9367\/revisions\/15584"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/6350"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=9367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=9367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=9367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}