How do you solve the equation in detail :: 12(2w-3)=6w<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the equation ( 12(2w – 3) = 6w ), we\u2019ll simplify and isolate the variable ( w ). Here\u2019s a step-by-step approach with a detailed explanation:<\/p>\n\n\n\n Start by expanding the left side of the equation: Our goal is to isolate ( w ) on one side of the equation. To do this, move ( 6w ) from the right side to the left side by subtracting ( 6w ) from both sides: Now, add ( 36 ) to both sides to move the constant term to the right: Now that we have ( 18w = 36 ), we can solve for ( w ) by dividing both sides by ( 18 ): The solution to the equation is ( w = 2 ).<\/p>\n\n\n\n This solution involves applying fundamental algebraic principles, particularly the distributive property, combining like terms, and isolating the variable. First, distributing ( 12 ) across the terms in the parentheses simplifies the left side of the equation. This step is crucial because it eliminates the parentheses, allowing us to deal directly with terms involving ( w ).<\/p>\n\n\n\n Next, by moving all terms involving ( w ) to one side, we ensure that all ( w )-terms are consolidated, making it easier to isolate ( w ) by combining like terms. The final steps involve using addition and division to isolate ( w ), a process known as \u201csolving for ( w )\u201d because it leaves ( w ) alone on one side of the equation.<\/p>\n\n\n\n Verifying the solution by substituting ( w = 2 ) back into the original equation confirms that both sides are equal, showing the correctness of the answer. Thus, the solution to ( 12(2w – 3) = 6w ) is ( w = 2 ).<\/p>\n","protected":false},"excerpt":{"rendered":" How do you solve the equation in detail :: 12(2w-3)=6w The Correct Answer and Explanation is: To solve the equation ( 12(2w – 3) = 6w ), we\u2019ll simplify and isolate the variable ( w ). Here\u2019s a step-by-step approach with a detailed explanation: Step 1: Distribute 12 to terms inside the parentheses Start by […]<\/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-163402","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163402","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=163402"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163402\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Distribute 12 to terms inside the parentheses<\/h3>\n\n\n\n
[
12 \\cdot (2w – 3) = 6w
]
Using the distributive property, multiply ( 12 ) by each term inside the parentheses:
[
12 \\cdot 2w – 12 \\cdot 3 = 6w
]
[
24w – 36 = 6w
]<\/p>\n\n\n\nStep 2: Move all terms involving ( w ) to one side of the equation<\/h3>\n\n\n\n
[
24w – 6w – 36 = 0
]
Simplify by combining like terms on the left side:
[
18w – 36 = 0
]<\/p>\n\n\n\nStep 3: Isolate the term with ( w )<\/h3>\n\n\n\n
[
18w = 36
]<\/p>\n\n\n\nStep 4: Solve for ( w )<\/h3>\n\n\n\n
[
w = \\frac{36}{18}
]
[
w = 2
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
Detailed Explanation<\/h3>\n\n\n\n