{"id":230354,"date":"2025-06-09T10:52:45","date_gmt":"2025-06-09T10:52:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230354"},"modified":"2025-06-09T10:52:48","modified_gmt":"2025-06-09T10:52:48","slug":"5d-22-d-31-d-1-solve-for-d","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/5d-22-d-31-d-1-solve-for-d\/","title":{"rendered":"5d + 2(2 – d) = 3(1 + d) + 1 Solve for d"},"content":{"rendered":"\n

5d + 2(2 – d) = 3(1 + d) + 1 Solve for d<\/p>\n\n\n\n

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

Let’s solve the equation step by step:<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n

5d+2(2\u2212d)=3(1+d)+15d + 2(2 – d) = 3(1 + d) + 15d+2(2\u2212d)=3(1+d)+1<\/p>\n\n\n\n

Step 1: Expand both sides<\/h3>\n\n\n\n

Distribute the constants outside the parentheses:<\/p>\n\n\n\n

Left side:<\/strong> 5d+2(2\u2212d)=5d+4\u22122d=(5d\u22122d)+4=3d+45d + 2(2 – d) = 5d + 4 – 2d = (5d – 2d) + 4 = 3d + 45d+2(2\u2212d)=5d+4\u22122d=(5d\u22122d)+4=3d+4<\/p>\n\n\n\n

Right side:<\/strong> 3(1+d)+1=3+3d+1=3d+43(1 + d) + 1 = 3 + 3d + 1 = 3d + 43(1+d)+1=3+3d+1=3d+4<\/p>\n\n\n\n

Now we have: 3d+4=3d+43d + 4 = 3d + 43d+4=3d+4<\/p>\n\n\n\n

Step 2: Subtract 3d+43d + 43d+4 from both sides<\/h3>\n\n\n\n

3d+4\u2212(3d+4)=0\u21d20=03d + 4 – (3d + 4) = 0 \\Rightarrow 0 = 03d+4\u2212(3d+4)=0\u21d20=0<\/p>\n\n\n\n

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

There is no unique solution<\/strong> \u2014 this equation is true for all values of ddd<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

The given equation is: 5d+2(2\u2212d)=3(1+d)+15d + 2(2 – d) = 3(1 + d) + 15d+2(2\u2212d)=3(1+d)+1<\/p>\n\n\n\n

To solve for ddd, we start by applying the distributive property, simplifying each side of the equation.<\/p>\n\n\n\n

On the left-hand side<\/strong>, 2(2\u2212d)2(2 – d)2(2\u2212d) becomes 4\u22122d4 – 2d4\u22122d. Adding this to 5d5d5d gives: 5d+4\u22122d=3d+45d + 4 – 2d = 3d + 45d+4\u22122d=3d+4<\/p>\n\n\n\n

On the right-hand side<\/strong>, 3(1+d)3(1 + d)3(1+d) becomes 3+3d3 + 3d3+3d, and adding 1 gives: 3+3d+1=3d+43 + 3d + 1 = 3d + 43+3d+1=3d+4<\/p>\n\n\n\n

After simplifying both sides, we get the same expression: 3d+4=3d+43d + 4 = 3d + 43d+4=3d+4<\/p>\n\n\n\n

This equation tells us that both sides are identical. When we try to isolate the variable ddd, we subtract 3d+43d + 43d+4 from both sides: (3d+4)\u2212(3d+4)=0\u21d20=0(3d + 4) – (3d + 4) = 0 \\Rightarrow 0 = 0(3d+4)\u2212(3d+4)=0\u21d20=0<\/p>\n\n\n\n

This result is a true statement<\/strong> and does not depend on the value of ddd. It implies that the original equation is always true<\/strong>, regardless of the value of ddd. Therefore, every real number is a solution<\/strong>. Such equations are called identities<\/strong>.<\/p>\n\n\n\n

In contrast, if the result had been a false statement (like 0=50 = 50=5), it would mean there is no solution<\/strong>. If we had isolated ddd and found a specific value (like d=2d = 2d=2), the equation would have had one solution<\/strong>.<\/p>\n\n\n\n

Here, since the equation is always true, the solution is:<\/p>\n\n\n\n

\n

All real numbers.<\/strong><\/p>\n\n\n\n

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

5d + 2(2 – d) = 3(1 + d) + 1 Solve for d The Correct Answer and Explanation is: Let’s solve the equation step by step: Given: 5d+2(2\u2212d)=3(1+d)+15d + 2(2 – d) = 3(1 + d) + 15d+2(2\u2212d)=3(1+d)+1 Step 1: Expand both sides Distribute the constants outside the parentheses: Left side: 5d+2(2\u2212d)=5d+4\u22122d=(5d\u22122d)+4=3d+45d + 2(2 […]<\/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-230354","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230354","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=230354"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230354\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}