{"id":9016,"date":"2017-05-01T15:02:19","date_gmt":"2017-05-01T15:02:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9016"},"modified":"2020-05-01T23:58:32","modified_gmt":"2020-05-01T23:58:32","slug":"summary-solve-equations-using-the-subtraction-and-addition-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/chapter\/summary-solve-equations-using-the-subtraction-and-addition-properties-of-equality\/","title":{"raw":"Summary: Solving Equations Using the Subtraction and Addition Properties of Equality","rendered":"Summary: Solving Equations Using the Subtraction and Addition Properties of Equality"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>Determine whether a number is a solution to an equation.<\/strong>\r\n<ol id=\"eip-id1170325336254\" 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.<\/li>\r\n<\/ol>\r\n<p style=\"padding-left: 60px\">If it is true, the number is a solution.\r\nIf it is not true, the number is not a solution.<\/p>\r\n<strong>Subtraction and Addition Properties of Equality<\/strong>\r\n<ul id=\"eip-id1170322764024\">\r\n \t<li><strong>Subtraction Property of Equality<\/strong><\/li>\r\n<\/ul>\r\n<p style=\"padding-left: 90px\">For all real numbers <em> a, b,<\/em> and <em>c<\/em>,\r\nif <em> a = b<\/em> then [latex]a-c=b-c[\/latex] .<\/p>\r\n\r\n<ul id=\"eip-id1170322764024\">\r\n \t<li><strong>Addition Property of Equality<\/strong><\/li>\r\n<\/ul>\r\n<p style=\"padding-left: 90px\">For all real numbers <em> a, b,<\/em> and <em>c<\/em>,\r\nif <em> a = b<\/em> then [latex]a+c=b+c[\/latex] .<\/p>\r\n\r\n<ul>\r\n \t<li><strong>Translate a word sentence to an algebraic equation.<\/strong>\r\n<ol id=\"eip-id1170324011027\" class=\"stepwise\">\r\n \t<li>Locate the \"equals\" word(s). Translate to an equal sign.<\/li>\r\n \t<li>Translate the words to the left of the \"equals\" word(s) into an algebraic expression.<\/li>\r\n \t<li>Translate the words to the right of the \"equals\" word(s) into an algebraic expression.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<ul id=\"eip-937\">\r\n \t<li><strong>Problem-solving strategy<\/strong>\r\n<ol id=\"eip-id1170325411872\" class=\"stepwise\">\r\n \t<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\r\n \t<li>Identify what you are looking for.<\/li>\r\n \t<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\r\n \t<li>Solve the equation using good algebra techniques.<\/li>\r\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li>Answer the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1170326208984\" class=\"definition\">\r\n \t<dt><strong>solution of an equation<\/strong><\/dt>\r\n \t<dd id=\"fs-id1170323908665\">A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/dd>\r\n<\/dl>\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>\r\n&nbsp;","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>Determine whether a number is a solution to an equation.<\/strong><\/p>\n<ol id=\"eip-id1170325336254\" 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.<\/li>\n<\/ol>\n<p style=\"padding-left: 60px\">If it is true, the number is a solution.<br \/>\nIf it is not true, the number is not a solution.<\/p>\n<p><strong>Subtraction and Addition Properties of Equality<\/strong><\/p>\n<ul id=\"eip-id1170322764024\">\n<li><strong>Subtraction Property of Equality<\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 90px\">For all real numbers <em> a, b,<\/em> and <em>c<\/em>,<br \/>\nif <em> a = b<\/em> then [latex]a-c=b-c[\/latex] .<\/p>\n<ul id=\"eip-id1170322764024\">\n<li><strong>Addition Property of Equality<\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 90px\">For all real numbers <em> a, b,<\/em> and <em>c<\/em>,<br \/>\nif <em> a = b<\/em> then [latex]a+c=b+c[\/latex] .<\/p>\n<ul>\n<li><strong>Translate a word sentence to an algebraic equation.<\/strong>\n<ol id=\"eip-id1170324011027\" class=\"stepwise\">\n<li>Locate the &#8220;equals&#8221; word(s). Translate to an equal sign.<\/li>\n<li>Translate the words to the left of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<li>Translate the words to the right of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<ul id=\"eip-937\">\n<li><strong>Problem-solving strategy<\/strong>\n<ol id=\"eip-id1170325411872\" class=\"stepwise\">\n<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n<li>Identify what you are looking for.<\/li>\n<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1170326208984\" class=\"definition\">\n<dt><strong>solution of an equation<\/strong><\/dt>\n<dd id=\"fs-id1170323908665\">A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.<\/dd>\n<\/dl>\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<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-9016\">\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":6,"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":"a737dbbe-836f-4ad0-afe3-1ccbd590e034","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9016","chapter","type-chapter","status-publish","hentry"],"part":7476,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9016","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\/9016\/revisions"}],"predecessor-version":[{"id":16016,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9016\/revisions\/16016"}],"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\/9016\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/media?parent=9016"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9016"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/contributor?post=9016"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/wp-json\/wp\/v2\/license?post=9016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}