{"id":225847,"date":"2025-06-04T16:23:09","date_gmt":"2025-06-04T16:23:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225847"},"modified":"2025-06-04T16:23:11","modified_gmt":"2025-06-04T16:23:11","slug":"solve-3-x-4-7-4-5-x-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/solve-3-x-4-7-4-5-x-12\/","title":{"rendered":"solve 3 X\/4 &#8211; 7 \/4 = 5 x + 12"},"content":{"rendered":"\n<p>solve 3 X\/4 &#8211; 7 \/4 = 5 x + 12<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given Equation:<\/strong><\/h3>\n\n\n\n<p>3&#215;4\u221274=5x+12\\frac{3x}{4} &#8211; \\frac{7}{4} = 5x + 12<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Eliminate fractions<\/strong><\/h3>\n\n\n\n<p>Multiply every term by 4 to eliminate the denominators: 4(3&#215;4\u221274)=4(5x+12)4 \\left( \\frac{3x}{4} &#8211; \\frac{7}{4} \\right) = 4(5x + 12) 3x\u22127=20x+483x &#8211; 7 = 20x + 48<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Get all x terms on one side<\/strong><\/h3>\n\n\n\n<p>Subtract 3x3x from both sides: \u22127=17x+48-7 = 17x + 48<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Move constants to the other side<\/strong><\/h3>\n\n\n\n<p>Subtract 48 from both sides: \u221255=17x-55 = 17x<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Solve for x<\/strong><\/h3>\n\n\n\n<p>x=\u22125517x = \\frac{-55}{17}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u2705 Final Answer:<\/h2>\n\n\n\n<p>x=\u22125517\\boxed{x = \\frac{-55}{17}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u270d\ufe0f Explanation <\/h2>\n\n\n\n<p>To solve the equation 3&#215;4\u221274=5x+12\\frac{3x}{4} &#8211; \\frac{7}{4} = 5x + 12, we begin by eliminating the fractions to simplify our work. Both fractional terms on the left have a denominator of 4, so we multiply every term in the equation by 4. This clears the denominators: 4(3&#215;4\u221274)=4(5x+12)\u21d23x\u22127=20x+484 \\left( \\frac{3x}{4} &#8211; \\frac{7}{4} \\right) = 4(5x + 12) \\Rightarrow 3x &#8211; 7 = 20x + 48<\/p>\n\n\n\n<p>This equation is much simpler. Next, we isolate the variable. To move all x terms to one side, we subtract 3x3x from both sides: \u22127=17x+48-7 = 17x + 48<\/p>\n\n\n\n<p>Now, we isolate the term with x by removing the constant on the right side. Subtract 48 from both sides: \u221255=17x-55 = 17x<\/p>\n\n\n\n<p>Finally, divide both sides by 17 to solve for x: x=\u22125517x = \\frac{-55}{17}<\/p>\n\n\n\n<p>This fraction is already in simplest form, and there\u2019s no need to convert it to a decimal unless specifically required. Leaving it as an improper fraction is acceptable in algebra.<\/p>\n\n\n\n<p>This problem illustrates how important it is to first eliminate fractions to simplify an equation. Then, using inverse operations (subtracting and dividing), we rearrange the equation step by step until x is isolated. Always check that each step maintains the balance of the equation. In the end, careful arithmetic and logical steps lead us to the correct solution: x=\u22125517\\boxed{x = \\frac{-55}{17}}.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-43.jpeg\" alt=\"\" class=\"wp-image-225848\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>solve 3 X\/4 &#8211; 7 \/4 = 5 x + 12 The Correct Answer and Explanation is: Given Equation: 3&#215;4\u221274=5x+12\\frac{3x}{4} &#8211; \\frac{7}{4} = 5x + 12 Step 1: Eliminate fractions Multiply every term by 4 to eliminate the denominators: 4(3&#215;4\u221274)=4(5x+12)4 \\left( \\frac{3x}{4} &#8211; \\frac{7}{4} \\right) = 4(5x + 12) 3x\u22127=20x+483x &#8211; 7 = 20x + [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-225847","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=225847"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225847\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}