{"id":255772,"date":"2025-07-13T08:55:41","date_gmt":"2025-07-13T08:55:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=255772"},"modified":"2025-07-13T08:55:43","modified_gmt":"2025-07-13T08:55:43","slug":"solve-for-x-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/13\/solve-for-x-5\/","title":{"rendered":"Solve for x"},"content":{"rendered":"\n

8\/9 (54x – 36) + 2 = -3\/4(-40 + 16x) + 90x. Solve for x<\/p>\n\n\n\n

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

To solve the equation 89(54x\u221236)+2=\u221234(\u221240+16x)+90x\\frac{8}{9}(54x – 36) + 2 = \\frac{-3}{4}(-40 + 16x) + 90×98\u200b(54x\u221236)+2=4\u22123\u200b(\u221240+16x)+90x, we\u2019ll go step by step:<\/p>\n\n\n\n

Step 1: Distribute the constants<\/h3>\n\n\n\n

Start by distributing the fractions on both sides.<\/p>\n\n\n\n

Left-hand side:<\/h4>\n\n\n\n

89(54x\u221236)+2\\frac{8}{9}(54x – 36) + 298\u200b(54x\u221236)+2<\/p>\n\n\n\n

Distribute 89\\frac{8}{9}98\u200b to both terms inside the parentheses: 89\u00d754x=8\u00d754×9=48x\\frac{8}{9} \\times 54x = \\frac{8 \\times 54x}{9} = 48×98\u200b\u00d754x=98\u00d754x\u200b=48x 89\u00d7\u221236=\u22128\u00d7369=\u221232\\frac{8}{9} \\times -36 = \\frac{-8 \\times 36}{9} = -3298\u200b\u00d7\u221236=9\u22128\u00d736\u200b=\u221232<\/p>\n\n\n\n

So, the left-hand side becomes: 48x\u221232+2=48x\u22123048x – 32 + 2 = 48x – 3048x\u221232+2=48x\u221230<\/p>\n\n\n\n

Right-hand side:<\/h4>\n\n\n\n

\u221234(\u221240+16x)+90x\\frac{-3}{4}(-40 + 16x) + 90×4\u22123\u200b(\u221240+16x)+90x<\/p>\n\n\n\n

Distribute \u221234\\frac{-3}{4}4\u22123\u200b to both terms inside the parentheses: \u221234\u00d7\u221240=1204=30\\frac{-3}{4} \\times -40 = \\frac{120}{4} = 304\u22123\u200b\u00d7\u221240=4120\u200b=30 \u221234\u00d716x=\u221248×4=\u221212x\\frac{-3}{4} \\times 16x = \\frac{-48x}{4} = -12×4\u22123\u200b\u00d716x=4\u221248x\u200b=\u221212x<\/p>\n\n\n\n

So, the right-hand side becomes: 30\u221212x+90x=30+78×30 – 12x + 90x = 30 + 78×30\u221212x+90x=30+78x<\/p>\n\n\n\n

Step 2: Set up the simplified equation<\/h3>\n\n\n\n

Now we can rewrite the equation as: 48x\u221230=30+78x48x – 30 = 30 + 78x48x\u221230=30+78x<\/p>\n\n\n\n

Step 3: Move all terms involving xxx to one side<\/h3>\n\n\n\n

Subtract 48x48x48x from both sides: \u221230=30+30x-30 = 30 + 30x\u221230=30+30x<\/p>\n\n\n\n

Step 4: Move the constant to the other side<\/h3>\n\n\n\n

Subtract 303030 from both sides: \u221260=30x-60 = 30x\u221260=30x<\/p>\n\n\n\n

Step 5: Solve for xxx<\/h3>\n\n\n\n

Divide both sides by 30: x=\u22126030=\u22122x = \\frac{-60}{30} = -2x=30\u221260\u200b=\u22122<\/p>\n\n\n\n

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

x=\u22122x = -2x=\u22122<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n
    \n
  • The equation initially involved distributing constants across terms.<\/li>\n\n\n\n
  • After distributing, I combined like terms on both sides.<\/li>\n\n\n\n
  • I then moved all terms involving xxx to one side and constants to the other.<\/li>\n\n\n\n
  • The final result is x=\u22122x = -2x=\u22122, which satisfies the original equation.<\/li>\n<\/ul>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    8\/9 (54x – 36) + 2 = -3\/4(-40 + 16x) + 90x. Solve for x The Correct Answer and Explanation is: To solve the equation 89(54x\u221236)+2=\u221234(\u221240+16x)+90x\\frac{8}{9}(54x – 36) + 2 = \\frac{-3}{4}(-40 + 16x) + 90×98\u200b(54x\u221236)+2=4\u22123\u200b(\u221240+16x)+90x, we\u2019ll go step by step: Step 1: Distribute the constants Start by distributing the fractions on both sides. Left-hand […]<\/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-255772","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255772","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=255772"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255772\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}