Let’s solve the equation step by step:<\/p>\n\n\n\n
Given: 4xx\u22123=12x\u22123+7\\frac{4x}{x-3} = \\frac{12}{x-3} + 7x\u221234x\u200b=x\u2212312\u200b+7<\/p>\n\n\n\n
Step 1: Eliminate the denominator<\/h3>\n\n\n\n
Since both sides have a denominator of x\u22123x – 3x\u22123, we can multiply both sides of the equation by x\u22123x – 3x\u22123, assuming x\u22603x \\neq 3x\ue020=3 to avoid division by zero. 4x=12+7(x\u22123)4x = 12 + 7(x – 3)4x=12+7(x\u22123)<\/p>\n\n\n\n
Step 2: Simplify the equation<\/h3>\n\n\n\n
Expand the right-hand side: 4x=12+7(x\u22123)4x = 12 + 7(x – 3)4x=12+7(x\u22123)<\/p>\n\n\n\n
Distribute the 7: 4x=12+7x\u2212214x = 12 + 7x – 214x=12+7x\u221221<\/p>\n\n\n\n
Now, simplify the constants: 4x=7x\u221294x = 7x – 94x=7x\u22129<\/p>\n\n\n\n
Step 3: Move terms involving xxx to one side<\/h3>\n\n\n\n
Subtract 7x7x7x from both sides: 4x\u22127x=\u221294x – 7x = -94x\u22127x=\u22129<\/p>\n\n\n\n
Simplify: \u22123x=\u22129-3x = -9\u22123x=\u22129<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
Divide both sides by -3: x=3x = 3x=3<\/p>\n\n\n\n
Step 5: Check for extraneous solutions<\/h3>\n\n\n\n
We need to check if x=3x = 3x=3 is valid in the original equation. If x=3x = 3x=3, the denominators in the original equation would become zero, which would make the equation undefined.<\/p>\n\n\n\n
Therefore, x=3x = 3x=3 is not<\/strong> a valid solution.<\/p>\n\n\n\n Since the solution leads to an invalid value (because it makes the denominator zero), the equation has no solution<\/strong>. This type of equation is known as an inconsistent equation<\/strong> because there is no value for xxx that satisfies it.<\/p>\n\n\n\n In summary:<\/p>\n\n\n\n Solve the equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. (4x)\/(x-3)=(12)\/(x-3)+7 The Correct Answer and Explanation is: Let’s solve the equation step by step: Given: 4xx\u22123=12x\u22123+7\\frac{4x}{x-3} = \\frac{12}{x-3} + 7x\u221234x\u200b=x\u2212312\u200b+7 Step 1: Eliminate the denominator Since both sides have a denominator of x\u22123x – 3x\u22123, we can […]<\/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-248412","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248412","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=248412"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248412\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Conclusion<\/h3>\n\n\n\n
\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-225.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"