{"id":234267,"date":"2025-06-14T03:17:13","date_gmt":"2025-06-14T03:17:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234267"},"modified":"2025-06-14T03:17:15","modified_gmt":"2025-06-14T03:17:15","slug":"the-product-of-a-number-and-4-is-the-sum-of-the-number-and-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/the-product-of-a-number-and-4-is-the-sum-of-the-number-and-4\/","title":{"rendered":"The product of a number and 4 is the sum of the number and 4."},"content":{"rendered":"\n

AThe product of a number and 4 is the sum of the number and 4. Find the number. X = b. Write an algebraic expression for the following phrase. Use x to represent the unknown number. 6 less than two times a number.<\/p>\n\n\n\n

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

a. The product of a number and 4 is the sum of the number and 4. Find the number.<\/h3>\n\n\n\n

Let the unknown number be x<\/strong>.<\/p>\n\n\n\n

We are told:<\/p>\n\n\n\n

\n

The product of a number and 4
= The sum of the number and 4<\/p>\n<\/blockquote>\n\n\n\n

This translates to the equation: 4x=x+44x = x + 44x=x+4<\/p>\n\n\n\n

Now solve the equation:<\/p>\n\n\n\n

Step 1:<\/strong> Subtract x<\/strong> from both sides: 4x\u2212x=x+4\u2212x4x – x = x + 4 – x4x\u2212x=x+4\u2212x 3x=43x = 43x=4<\/p>\n\n\n\n

Step 2:<\/strong> Divide both sides by 3: x=43x = \\frac{4}{3}x=34\u200b<\/p>\n\n\n\n

\u2705 Answer for part a:<\/strong> x=43\\boxed{x = \\frac{4}{3}}x=34\u200b\u200b<\/p>\n\n\n\n

\n\n\n\n

b. Write an algebraic expression for the following phrase:<\/h3>\n\n\n\n

“6 less than two times a number”<\/strong><\/p>\n\n\n\n

Let the unknown number be x<\/strong>.<\/p>\n\n\n\n

\n

“Two times a number” means:<\/p>\n<\/blockquote>\n\n\n\n

2x2x2x<\/p>\n\n\n\n

\n

“6 less than” means subtract 6 from<\/strong> that quantity (important: “less than” reverses the order of subtraction)<\/p>\n<\/blockquote>\n\n\n\n

So, the expression becomes: 2x\u221262x – 62x\u22126<\/p>\n\n\n\n

\u2705 Answer for part b:<\/strong> 2x\u22126\\boxed{2x – 6}2x\u22126\u200b<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udcd8 300-Word Style Explanation:<\/h3>\n\n\n\n

In algebra, we often translate word problems into equations or expressions using variables. A variable, like x<\/strong>, stands for an unknown value that we are trying to find or represent.<\/p>\n\n\n\n

Part a:<\/h4>\n\n\n\n

The statement says “the product of a number and 4”<\/strong>, which means we multiply the number by 4, or 4x<\/strong>. It also says this product is equal to the sum of the number and 4<\/strong>, or x + 4<\/strong>. We then write this relationship as an equation: 4x=x+44x = x + 44x=x+4<\/p>\n\n\n\n

To solve, we use inverse operations. Subtract x<\/strong> from both sides to isolate like terms: 4x\u2212x=3x=44x – x = 3x = 44x\u2212x=3x=4<\/p>\n\n\n\n

Then divide both sides by 3: x=43x = \\frac{4}{3}x=34\u200b<\/p>\n\n\n\n

Part b:<\/h4>\n\n\n\n

The phrase “6 less than two times a number”<\/strong> requires careful interpretation. Two times a number<\/strong> is written as 2x<\/strong>. The phrase “6 less than”<\/strong> means subtract 6 from the previous amount. So, the expression becomes: 2x\u221262x – 62x\u22126<\/p>\n\n\n\n

In both parts, understanding the language used is key to writing correct mathematical models. Phrases like “less than”<\/em>, “more than”<\/em>, “product of”<\/em>, and “sum of”<\/em> each have specific meanings that help guide the setup of the expression or equation.<\/p>\n\n\n\n

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

AThe product of a number and 4 is the sum of the number and 4. Find the number. X = b. Write an algebraic expression for the following phrase. Use x to represent the unknown number. 6 less than two times a number. The Correct Answer and Explanation is: a. The product of a number […]<\/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-234267","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234267","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=234267"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234267\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}