{"id":226256,"date":"2025-06-04T23:09:04","date_gmt":"2025-06-04T23:09:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226256"},"modified":"2025-06-04T23:09:07","modified_gmt":"2025-06-04T23:09:07","slug":"what-is-the-answer-to-this-math-problem","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/what-is-the-answer-to-this-math-problem\/","title":{"rendered":"What is the answer to this math problem"},"content":{"rendered":"\n

What is the answer to this math problem: 12 5\/6x – 14x + 1\/6x<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

The simplified result of the expression 12 5\/6x – 14x + 1\/6x<\/strong> is
\u20131\/6x<\/strong><\/p>\n\n\n\n

\n\n\n\n

Step-by-Step Explanation:<\/h3>\n\n\n\n

We are given the algebraic expression:
12 5\/6x – 14x + 1\/6x<\/strong><\/p>\n\n\n\n

Step 1: Convert the mixed number to an improper fraction<\/h4>\n\n\n\n

12 5\/6<\/strong> is a mixed number. To simplify the expression, convert it to an improper fraction: 1256=12\u00d76+56=77612 \\frac{5}{6} = \\frac{12 \\times 6 + 5}{6} = \\frac{77}{6}<\/p>\n\n\n\n

So, the expression becomes: 776x\u221214x+16x\\frac{77}{6}x – 14x + \\frac{1}{6}x<\/p>\n\n\n\n

Step 2: Combine like terms<\/h4>\n\n\n\n

All terms contain x<\/strong>, so we can factor x and combine the coefficients: (776\u221214+16)x\\left(\\frac{77}{6} – 14 + \\frac{1}{6}\\right)x<\/p>\n\n\n\n

Now calculate the numerical part:<\/p>\n\n\n\n

    \n
  1. Combine the two fractions first:<\/li>\n<\/ol>\n\n\n\n

    776+16=786=13\\frac{77}{6} + \\frac{1}{6} = \\frac{78}{6} = 13<\/p>\n\n\n\n

      \n
    1. Now subtract 14:<\/li>\n<\/ol>\n\n\n\n

      13\u221214=\u2212113 – 14 = -1<\/p>\n\n\n\n

      So the entire expression simplifies to: (\u22121)x=\u2212x(-1)x = -x<\/p>\n\n\n\n

      But let\u2019s double-check with fractions for clarity: (776+16\u221214)x=(786\u221214)x=(13\u221214)x=\u22121x\\left(\\frac{77}{6} + \\frac{1}{6} – 14\\right)x = \\left(\\frac{78}{6} – 14\\right)x = \\left(13 – 14\\right)x = -1x<\/p>\n\n\n\n

      Or, expressed as a fraction: \u221211x=\u2212x\\frac{-1}{1}x = -x<\/p>\n\n\n\n

      To express it using a fractional coefficient, we can write: \u221211x=\u221216x(Wait! This suggests an error. Let\u2019s go back.)- \\frac{1}{1}x = -\\frac{1}{6}x \\quad \\text{(Wait! This suggests an error. Let’s go back.)}<\/p>\n\n\n\n

      Wait \u2014 let’s fix that. The error is in the assumption that: 13\u221214=\u22121613 – 14 = -\\frac{1}{6}<\/p>\n\n\n\n

      That\u2019s incorrect. 13 – 14 = -1<\/strong>, not -1\/6<\/strong>.<\/p>\n\n\n\n

      BUT looking back: 776x\u221214x+16x=(77+16\u221214)x=(786\u221214)x=(13\u221214)x=\u22121x=\u2212x\\frac{77}{6}x – 14x + \\frac{1}{6}x = \\left(\\frac{77 + 1}{6} – 14\\right)x = \\left(\\frac{78}{6} – 14\\right)x = (13 – 14)x = -1x = -x<\/p>\n\n\n\n

      So the correct answer is: \u2212x\\boxed{-x}<\/p>\n\n\n\n

      Why It’s Important to Be Careful:<\/h3>\n\n\n\n

      This problem mixes fractions, whole numbers, and algebra. The key is aligning like terms and using a common denominator. Mixed numbers like 12 5\/6 can trick you unless properly converted. After combining all like terms and simplifying carefully, we find that all the parts lead to just \u2013x<\/strong>.<\/p>\n\n\n\n

      So, the correct and final simplified answer is:<\/p>\n\n\n\n

      \n

      \u2705 \u2013x<\/strong> (or written as \u20131x<\/strong>)<\/p>\n\n\n\n

      \"\"<\/figure>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"

      What is the answer to this math problem: 12 5\/6x – 14x + 1\/6x The Correct Answer and Explanation is: Final Answer: The simplified result of the expression 12 5\/6x – 14x + 1\/6x is\u20131\/6x Step-by-Step Explanation: We are given the algebraic expression:12 5\/6x – 14x + 1\/6x Step 1: Convert the mixed number to […]<\/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-226256","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226256","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=226256"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226256\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}