{"id":189038,"date":"2025-02-08T11:06:35","date_gmt":"2025-02-08T11:06:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=189038"},"modified":"2025-02-08T11:06:38","modified_gmt":"2025-02-08T11:06:38","slug":"solve-each-inequality","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/08\/solve-each-inequality\/","title":{"rendered":"Solve each inequality"},"content":{"rendered":"\n<p>2.1 EXERCISES Solve each inequality. 2. 4x-8 > 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + &#8211; &#8212; 12 4 5. 6. 8x &#8211; 72 7x-2 2 3 4. d + 3 2x + 7 10. 6x -+ 25x -5 11. &#8211; 8 4 18 6 13. 2x-2 3(2x &#8211; 5) 19. 2(2-5) 3(5-2y) 20. 3(2x-5) 8x-5 21. 2(3x &#8211; 1) > 3x+4 22. 3(x &#8211; 2)2-5(x-2) 23. *;** (2x+6) 3 25. 48+ x 2 5(2x + 4) \u2013 2x 26. 24 2 6x-2(3x &#8211; 5)+2x 27. 3(x &#8211; 8) &lt; 3x-1=&#8221;&#8221; 29.=&#8221;&#8221; -2(x+7)=&#8221;&#8221; 3(x+2)=&#8221;&#8221; 30.=&#8221;&#8221; 3(x-5)=&#8221;&#8221;>-(x+3) 31. 15x+354 32. 1&lt;>&lt; 12=&#8221;&#8221; or=&#8221;&#8221; x=&#8221;&#8221; +7=&#8221;&#8221;>10 38. x+4 -12 39. &#8211; 2xs-4 or 5x &#8211; 20 25 40. Si or xs-3 41. Os 2x-359 42. -552(x+4)58 43. -6&lt;=2x-1_2 45.=&#8221;&#8221; os=&#8221;&#8221; 5-2x=&#8221;&#8221; 5=&#8221;&#8221; give=&#8221;&#8221; call=&#8221;&#8221; neg=&#8221;&#8221; the=&#8221;&#8221; .4s2x+3=&#8221;&#8221; si=&#8221;&#8221; 47.=&#8221;&#8221; ssx+15-2=&#8221;&#8221; !=&#8221;&#8221; 1=&#8221;&#8221; win=&#8221;&#8221;>\u00a02+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + &#8211; &#8212; 12 4 5. 6. 8x &#8211; 72 7x-2 2&#8243; style=&amp;#39;width:332.4pt;height:249pt;rotation:90;visibility:visible; mso-wrap-style:square&amp;#39;> 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + &#8211; &#8212; 12 4 5. 6&#8243;><\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s solve each of the given inequalities step by step:<\/p>\n\n\n\n<p><strong>1. Solve: 3n &#8211; 9 &gt; 2n &#8211; 8<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 2n from both sides: 3n &#8211; 2n &#8211; 9 > 2n &#8211; 2n &#8211; 8, simplifying to n &#8211; 9 > -8.<\/li>\n\n\n\n<li>Add 9 to both sides: n &#8211; 9 + 9 > -8 + 9, simplifying to n > 1.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Solve: 4x &#8211; 8 &gt; 2 + 3x<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 3x from both sides: 4x &#8211; 3x &#8211; 8 > 2 + 3x &#8211; 3x, simplifying to x &#8211; 8 > 2.<\/li>\n\n\n\n<li>Add 8 to both sides: x &#8211; 8 + 8 > 2 + 8, simplifying to x > 10.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. Solve: 7x &#8211; 3 &gt; 6x &#8211; 2<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 6x from both sides: 7x &#8211; 6x &#8211; 3 > 6x &#8211; 6x &#8211; 2, simplifying to x &#8211; 3 > -2.<\/li>\n\n\n\n<li>Add 3 to both sides: x &#8211; 3 + 3 > -2 + 3, simplifying to x > 1.<\/li>\n<\/ul>\n\n\n\n<p><strong>4. Solve: d + 3 &lt; 2x + 7<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 3 from both sides: d + 3 &#8211; 3 &lt; 2x + 7 &#8211; 3, simplifying to d &lt; 2x + 4.<\/li>\n<\/ul>\n\n\n\n<p><strong>5. Solve: 8x &#8211; 7 &lt; 2x + 3<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 2x from both sides: 8x &#8211; 2x &#8211; 7 &lt; 2x &#8211; 2x + 3, simplifying to 6x &#8211; 7 &lt; 3.<\/li>\n\n\n\n<li>Add 7 to both sides: 6x &#8211; 7 + 7 &lt; 3 + 7, simplifying to 6x &lt; 10.<\/li>\n\n\n\n<li>Divide both sides by 6: 6x \/ 6 &lt; 10 \/ 6, simplifying to x &lt; 5\/3.<\/li>\n<\/ul>\n\n\n\n<p><strong>6. Solve: 8x &#8211; 7 &lt; 2x + 3<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract 2x from both sides: 8x &#8211; 2x &#8211; 7 &lt; 2x &#8211; 2x + 3, simplifying to 6x &#8211; 7 &lt; 3.<\/li>\n\n\n\n<li>Add 7 to both sides: 6x &#8211; 7 + 7 &lt; 3 + 7, simplifying to 6x &lt; 10.<\/li>\n\n\n\n<li>Divide both sides by 6: 6x \/ 6 &lt; 10 \/ 6, simplifying to x &lt; 5\/3.<\/li>\n<\/ul>\n\n\n\n<p><strong>7. Solve: 2x &#8211; 2 &lt; 3(2x &#8211; 5)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Expand the right side: 2x &#8211; 2 &lt; 6x &#8211; 15.<\/li>\n\n\n\n<li>Subtract 2x from both sides: 2x &#8211; 2 &#8211; 2x &lt; 6x &#8211; 15 &#8211; 2x, simplifying to -2 &lt; 4x &#8211; 15.<\/li>\n\n\n\n<li>Add 15 to both sides: -2 + 15 &lt; 4x &#8211; 15 + 15, simplifying to 13 &lt; 4x.<\/li>\n\n\n\n<li>Divide both sides by 4: 13 \/ 4 &lt; 4x \/ 4, simplifying to 13\/4 &lt; x.<\/li>\n<\/ul>\n\n\n\n<p><strong>8. Solve: 2(2 &#8211; 5) &lt; 3(5 &#8211; 2y)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify both sides: 2(-3) &lt; 3(5 &#8211; 2y), which simplifies to -6 &lt; 15 &#8211; 6y.<\/li>\n\n\n\n<li>Subtract 15 from both sides: -6 &#8211; 15 &lt; 15 &#8211; 15 &#8211; 6y, simplifying to -21 &lt; -6y.<\/li>\n\n\n\n<li>Divide both sides by -6: -21 \/ -6 &lt; -6y \/ -6, simplifying to 7\/2 > y.<\/li>\n\n\n\n<li>Since we divided by a negative number, the inequality sign flips.<\/li>\n<\/ul>\n\n\n\n<p><strong>9. Solve: 3(2x &#8211; 5) &lt; 8x &#8211; 5<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Expand both sides: 6x &#8211; 15 &lt; 8x &#8211; 5.<\/li>\n\n\n\n<li>Subtract 6x from both sides: 6x &#8211; 6x &#8211; 15 &lt; 8x &#8211; 6x &#8211; 5, simplifying to -15 &lt; 2x &#8211; 5.<\/li>\n\n\n\n<li>Add 5 to both sides: -15 + 5 &lt; 2x &#8211; 5 + 5, simplifying to -10 &lt; 2x.<\/li>\n\n\n\n<li>Divide both sides by 2: -10 \/ 2 &lt; 2x \/ 2, simplifying to -5 &lt; x.<\/li>\n<\/ul>\n\n\n\n<p><strong>10. Solve: 6x + 25x &#8211; 5 &lt; 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Combine like terms: 31x &#8211; 5 &lt; 0.<\/li>\n\n\n\n<li>Add 5 to both sides: 31x &#8211; 5 + 5 &lt; 0 + 5, simplifying to 31x &lt; 5.<\/li>\n\n\n\n<li>Divide both sides by 31: 31x \/ 31 &lt; 5 \/ 31, simplifying to x &lt; 5\/31.<\/li>\n<\/ul>\n\n\n\n<p><strong>11. Solve: -8 &lt; 4x &#8211; 18<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add 18 to both sides: -8 + 18 &lt; 4x &#8211; 18 + 18, simplifying to 10 &lt; 4x.<\/li>\n\n\n\n<li>Divide both sides by 4: 10 \/ 4 &lt; 4x \/ 4, simplifying to 5\/2 &lt; x.<\/li>\n<\/ul>\n\n\n\n<p><strong>12. Solve: 2x &#8211; 2 &lt; 3(2x &#8211; 5)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Expand both sides: 2x &#8211; 2 &lt; 6x &#8211;<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>2.1 EXERCISES Solve each inequality. 2. 4x-8 > 2+ 3x 3. 7x-3 > 6x-2 1. 3n-9 > 2n-8 1 1 53 y + &#8211; &#8212; 12 4 5. 6. 8x &#8211; 72 7x-2 2 3 4. d + 3 2x + 7 10. 6x -+ 25x -5 11. &#8211; 8 4 18 6 13. 2x-2 [&hellip;]<\/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-189038","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189038","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=189038"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189038\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189038"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189038"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189038"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}