{"id":2736,"date":"2025-08-13T18:33:33","date_gmt":"2025-08-13T18:33:33","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2736"},"modified":"2025-10-17T18:33:00","modified_gmt":"2025-10-17T18:33:00","slug":"trigonometric-identities-and-equations-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/trigonometric-identities-and-equations-background-youll-need-2\/","title":{"raw":"Trigonometric Identities and Equations: Background You'll Need 2","rendered":"Trigonometric Identities and Equations: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Solve linear equations using inverse operations<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<ol>\r\n \t<li>Solve [latex]3x + 5 = 11[\/latex].<\/li>\r\n \t<li>Solve [latex]-4x - 8 = 12[\/latex].<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"655379\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"655379\"]\r\n<ol>\r\n \t<li>Solve [latex]3x + 5 = 11[\/latex].\r\n\r\n[latex]\r\n\\begin{align}\r\n3x + 5 &amp;= 11 \\\\\r\n3x &amp;= 11 - 5 \\\\\r\n3x &amp;= 6 \\\\\r\nx &amp;= \\frac{6}{3} = 2\r\n\\end{align}\r\n[\/latex]<\/li>\r\n \t<li>Solve [latex]-4x - 8 = 12[\/latex].\r\n\r\n[latex]\r\n\\begin{align}\r\n-4x - 8 &amp;= 12 \\\\\r\n-4x &amp;= 12 + 8 \\\\\r\n-4x &amp;= 20 \\\\\r\nx &amp;=\u00a0 -5\r\n\\end{align}\r\n[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313761[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Solve linear equations using inverse operations<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<ol>\n<li>Solve [latex]3x + 5 = 11[\/latex].<\/li>\n<li>Solve [latex]-4x - 8 = 12[\/latex].<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q655379\">Show Solution<\/button><\/p>\n<div id=\"q655379\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Solve [latex]3x + 5 = 11[\/latex].\n<p>[latex]\\begin{align}  3x + 5 &= 11 \\\\  3x &= 11 - 5 \\\\  3x &= 6 \\\\  x &= \\frac{6}{3} = 2  \\end{align}[\/latex]<\/li>\n<li>Solve [latex]-4x - 8 = 12[\/latex].\n<p>[latex]\\begin{align}  -4x - 8 &= 12 \\\\  -4x &= 12 + 8 \\\\  -4x &= 20 \\\\  x &=\u00a0 -5  \\end{align}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313761\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313761&theme=lumen&iframe_resize_id=ohm313761&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":201,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2736"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":11,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2736\/revisions"}],"predecessor-version":[{"id":4718,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2736\/revisions\/4718"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/201"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2736\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2736"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2736"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2736"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}