{"id":45354,"date":"2025-07-01T06:07:21","date_gmt":"2025-07-01T06:07:21","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=45354"},"modified":"2025-07-01T06:07:23","modified_gmt":"2025-07-01T06:07:23","slug":"frac7x143-frac17-3x5-frac6x-4x2-53","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/frac7x143-frac17-3x5-frac6x-4x2-53\/","title":{"rendered":"\\frac{7x+14}{3} &#8211; \\frac{17-3x}{5} = \\frac{6x-4x+2-5}{3}"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\\frac{7x+14}{3} &#8211; \\frac{17-3x}{5} = \\frac{6x-4x+2-5}{3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve the given equation: 7x+143\u221217\u22123&#215;5=6x\u22124x+2\u221253\\frac{7x + 14}{3} &#8211; \\frac{17 &#8211; 3x}{5} = \\frac{6x &#8211; 4x + 2 &#8211; 5}{3}37x+14\u200b\u2212517\u22123x\u200b=36x\u22124x+2\u22125\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Simplify the right-hand side.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start by simplifying the expression on the right side. Combine like terms: 6x\u22124x+2\u22125=2x\u221236x &#8211; 4x + 2 &#8211; 5 = 2x &#8211; 36x\u22124x+2\u22125=2x\u22123<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So the equation becomes: 7x+143\u221217\u22123&#215;5=2x\u221233\\frac{7x + 14}{3} &#8211; \\frac{17 &#8211; 3x}{5} = \\frac{2x &#8211; 3}{3}37x+14\u200b\u2212517\u22123x\u200b=32x\u22123\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: Eliminate the denominators.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To eliminate the fractions, multiply through by the least common denominator (LCD) of 3 and 5, which is 15. Multiply both sides of the equation by 15: 15(7x+143)\u221215(17\u22123&#215;5)=15(2x\u221233)15 \\left( \\frac{7x + 14}{3} \\right) &#8211; 15 \\left( \\frac{17 &#8211; 3x}{5} \\right) = 15 \\left( \\frac{2x &#8211; 3}{3} \\right)15(37x+14\u200b)\u221215(517\u22123x\u200b)=15(32x\u22123\u200b)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3: Simplify the equation.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now simplify each term:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For the first term: 15\u00d77x+143=5(7x+14)=35x+7015 \\times \\frac{7x + 14}{3} = 5(7x + 14) = 35x + 7015\u00d737x+14\u200b=5(7x+14)=35x+70<\/li>\n\n\n\n<li>For the second term: 15\u00d717\u22123&#215;5=3(17\u22123x)=51\u22129&#215;15 \\times \\frac{17 &#8211; 3x}{5} = 3(17 &#8211; 3x) = 51 &#8211; 9&#215;15\u00d7517\u22123x\u200b=3(17\u22123x)=51\u22129x<\/li>\n\n\n\n<li>For the third term: 15\u00d72x\u221233=5(2x\u22123)=10x\u22121515 \\times \\frac{2x &#8211; 3}{3} = 5(2x &#8211; 3) = 10x &#8211; 1515\u00d732x\u22123\u200b=5(2x\u22123)=10x\u221215<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So the equation now becomes: 35x+70\u2212(51\u22129x)=10x\u22121535x + 70 &#8211; (51 &#8211; 9x) = 10x &#8211; 1535x+70\u2212(51\u22129x)=10x\u221215<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 4: Distribute the negative sign.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distribute the negative sign across the parentheses: 35x+70\u221251+9x=10x\u22121535x + 70 &#8211; 51 + 9x = 10x &#8211; 1535x+70\u221251+9x=10x\u221215<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify the left side: 35x+9x+70\u221251=10x\u22121535x + 9x + 70 &#8211; 51 = 10x &#8211; 1535x+9x+70\u221251=10x\u221215 44x+19=10x\u22121544x + 19 = 10x &#8211; 1544x+19=10x\u221215<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 5: Solve for xxx.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Move all terms involving xxx to one side and constants to the other side: 44x\u221210x=\u221215\u22121944x &#8211; 10x = -15 &#8211; 1944x\u221210x=\u221215\u221219<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify: 34x=\u22123434x = -3434x=\u221234<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now divide both sides by 34: x=\u22123434x = \\frac{-34}{34}x=34\u221234\u200b x=\u22121x = -1x=\u22121<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Final Answer:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The solution to the equation is x=\u22121x = -1x=\u22121<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-17.jpeg\" alt=\"\" class=\"wp-image-45355\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-17.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-17-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-17-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-17-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\\frac{7x+14}{3} &#8211; \\frac{17-3x}{5} = \\frac{6x-4x+2-5}{3} The Correct Answer and Explanation is: To solve the given equation: 7x+143\u221217\u22123&#215;5=6x\u22124x+2\u221253\\frac{7x + 14}{3} &#8211; \\frac{17 &#8211; 3x}{5} = \\frac{6x &#8211; 4x + 2 &#8211; 5}{3}37x+14\u200b\u2212517\u22123x\u200b=36x\u22124x+2\u22125\u200b Step 1: Simplify the right-hand side. Start by simplifying the expression on the right side. Combine like terms: 6x\u22124x+2\u22125=2x\u221236x &#8211; 4x + 2 &#8211; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-45354","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=45354"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45354\/revisions"}],"predecessor-version":[{"id":45356,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45354\/revisions\/45356"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}