{"id":39068,"date":"2025-06-26T18:53:35","date_gmt":"2025-06-26T18:53:35","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39068"},"modified":"2025-06-26T18:53:36","modified_gmt":"2025-06-26T18:53:36","slug":"jorge-solves-the-equation-4x%e2%88%92x2623x8-using-the-steps-below","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/jorge-solves-the-equation-4x%e2%88%92x2623x8-using-the-steps-below\/","title":{"rendered":"Jorge solves the equation\u00a04x\u2212(x+2)+6=2(3x+8)\u00a0using the steps below."},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Jorge solves the equation&nbsp;4x\u2212(x+2)+6=2(3x+8)&nbsp;using the steps below.<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-378.png\" alt=\"\" class=\"wp-image-39069\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-378.png 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-378-300x300.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-378-150x150.png 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-378-768x768.png 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is: <strong>Jorge incorrectly combined like terms.<\/strong><\/p>\n\n\n\n<p>In the equation<\/p>\n\n\n\n<p>4x\u2212(x+2)+6=2(3x+8)4x &#8211; (x + 2) + 6 = 2(3x + 8)<\/p>\n\n\n\n<p>the first step involves simplifying both sides. Jorge attempted this in Step 1 but made a critical error while simplifying the left-hand side.<\/p>\n\n\n\n<p>When you distribute the minus sign across the parentheses, the expression becomes:<\/p>\n\n\n\n<p>4x\u2212x\u22122+6=2(3x+8)4x &#8211; x &#8211; 2 + 6 = 2(3x + 8)<\/p>\n\n\n\n<p>Combining like terms correctly on the left gives:<\/p>\n\n\n\n<p>3x+4=6x+163x + 4 = 6x + 16<\/p>\n\n\n\n<p>Jorge, however, wrote Step 1 as:<\/p>\n\n\n\n<p>4x\u2212x+2+6=6x+164x &#8211; x + 2 + 6 = 6x + 16<\/p>\n\n\n\n<p>This indicates he forgot to distribute the minus sign to both xx and 22, and instead added 2 instead of subtracting it. As a result, the left-hand side was incorrectly simplified to 3x+83x + 8, leading to the wrong equation:<\/p>\n\n\n\n<p>3x+8=6x+163x + 8 = 6x + 16<\/p>\n\n\n\n<p>From this incorrect equation, his steps led him to a wrong value of x=83x = \\frac{8}{3}, which does not satisfy the original equation.<\/p>\n\n\n\n<p>When we use the correct form of the equation 3x+4=6x+163x + 4 = 6x + 16, solving it step by step:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>Subtract 3x3x from both sides:<\/li>\n<\/ol>\n\n\n\n<p>4=3x+164 = 3x + 16<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>Subtract 16 from both sides:<\/li>\n<\/ol>\n\n\n\n<p>\u221212=3x-12 = 3x<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>Divide both sides by 3:<\/li>\n<\/ol>\n\n\n\n<p>x=\u22124x = -4<\/p>\n\n\n\n<p>Therefore, the correct solution is x=\u22124x = -4. When substituted back, both sides of the original equation equal, confirming it is correct.<\/p>\n\n\n\n<p>Jorge\u2019s mistake stemmed from an error during distribution and simplification, which misled every step that followed.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1118.jpeg\" alt=\"\" class=\"wp-image-39070\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1118.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1118-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1118-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Jorge solves the equation&nbsp;4x\u2212(x+2)+6=2(3x+8)&nbsp;using the steps below. The Correct Answer and Explanation is: The correct answer is: Jorge incorrectly combined like terms. In the equation 4x\u2212(x+2)+6=2(3x+8)4x &#8211; (x + 2) + 6 = 2(3x + 8) the first step involves simplifying both sides. Jorge attempted this in Step 1 but made a critical error while [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39068","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39068","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39068"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39068\/revisions"}],"predecessor-version":[{"id":39071,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39068\/revisions\/39071"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}