{"id":453,"date":"2022-04-13T05:14:39","date_gmt":"2022-04-13T05:14:39","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=453"},"modified":"2025-08-19T18:25:36","modified_gmt":"2025-08-19T18:25:36","slug":"w-8-solve-multi-step-equations","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/w-8-solve-multi-step-equations\/","title":{"rendered":"W.8 Solve multi-step equations"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve multi-step equations<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwH6sXIbQ\/ZasbA3IoN46Qv-OMHJKzyw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwH6sXIbQ&#x2F;ZasbA3IoN46Qv-OMHJKzyw&#x2F;watch?utm_content=DAGwH6sXIbQ&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Class-8 Topic: Solve multi-step equations<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>What Are Multi-Step Equations?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> Equations that require <strong>two or more operations<\/strong> (addition, subtraction, multiplication, or division) to isolate the variable.<\/li>\n\n\n\n<li>Example: 3x+7=16 (needs subtraction and division to solve).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Steps to Solve Multi-Step Equations<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Simplify both sides<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Remove parentheses using <strong>Distributive Property<\/strong>:<br>a(b+c)=ab+ac<\/li>\n\n\n\n<li>Combine like terms (terms with the same variable or constants).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Move variable terms to one side<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>Addition or Subtraction Property of Equality<\/strong>:<br>If a=b, then a+c=b+c and a\u2212c=b\u2212c.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 3: Move constant terms to the other side<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Get constants on one side and variables on the other.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 4: Isolate the variable<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>Multiplication or Division Property of Equality<\/strong>:<br>If a=b, then a\u22c5c=b\u22c5c or  a\/c\u200b=b\/c\u200b (where c\u22600).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 5: Check your solution<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Substitute the value back into the original equation.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Example Problems with Solutions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Example 1:<\/strong><\/h4>\n\n\n\n<p>2(x+3)\u22124=10<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Distribute: 2x+6\u22124=10<\/li>\n\n\n\n<li>Combine like terms: 2x+2=10<\/li>\n\n\n\n<li>Subtract 2 from both sides: 2x=8<\/li>\n\n\n\n<li>Divide by 2: x=4<\/li>\n\n\n\n<li><strong>Check:<\/strong> 2(4+3)\u22124=14\u22124=10 \u2714<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Example 2:<\/strong><\/h4>\n\n\n\n<p>5x\u22127=3x+9<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Subtract 3xfrom both sides: 2x\u22127=9<\/li>\n\n\n\n<li>Add 7 to both sides: 2x=16<\/li>\n\n\n\n<li>Divide by 2: x=8<\/li>\n\n\n\n<li><strong>Check:<\/strong> 5(8)\u22127=33\u2714<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 3 (Fractions):<\/strong><\/h4>\n\n\n\n<p>x\/3+4=7<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Subtract 4: x\/3=3<\/li>\n\n\n\n<li>Multiply by 3: x=9<\/li>\n\n\n\n<li><strong>Check:<\/strong> 9\/3+4=3+4=7 \u2714<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Tips &amp; Tricks<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always <strong>simplify first<\/strong> before moving terms.<\/li>\n\n\n\n<li>If you see parentheses, <strong>distribute<\/strong> before anything else.<\/li>\n\n\n\n<li>Keep the <strong>variable positive<\/strong> when possible for easier solving.<\/li>\n\n\n\n<li>Check your answer to avoid mistakes.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Practice Questions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Solve each:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>4(x\u22122)=20<\/li>\n\n\n\n<li>3x+5=2x+9<\/li>\n\n\n\n<li>2&#215;5\u22124=6<\/li>\n\n\n\n<li>7\u22122(x\u22123)=1<\/li>\n\n\n\n<li>5x\u22123=2x+12<\/li>\n<\/ol>\n\n\n\n<p class=\"has-normal-font-size\">To solve for a variable, use inverse operations to undo the operations in the equation. Be sure to do the same operation to both sides of the equation.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b8d35d\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-583c3d268ca992363771950531c25c32\" style=\"color:#b00012\"><strong>Solve for&nbsp;<em>s<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-ea8f4d32c8d2c9f48497551ca9d5591b\" style=\"color:#b00012\">7 \u2212&nbsp;<em>s<\/em>&nbsp;= 2<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-a997eec2d2b906be003b19ac082b9fac\" style=\"color:#b00012\"><em>s<\/em>&nbsp;=&nbsp;&#8212;&#8212;<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ef597f5f7343649aa45c222b4314f507\">Solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-86ec5c034d504fed77e96412b64de3ca\">7 \u2212&nbsp;<em>s<\/em>&nbsp;=&nbsp;2<br>7 \u2212&nbsp;<em>s<\/em>&nbsp;+&nbsp;<em>s<\/em>&nbsp;=&nbsp;2 +&nbsp;<em>s          <\/em><em>Add&nbsp;s&nbsp;to both sides<\/em><br>7&nbsp;=&nbsp;2 +&nbsp;<em>s                              <\/em><em>Simplify<\/em><br>7 \u2212 2&nbsp;=&nbsp;2 +&nbsp;<em>s<\/em>&nbsp;\u2212 2               <em>Subtract 2 from both sides<\/em><br>5&nbsp;=&nbsp;<em>s                                                <\/em><em>Simplify<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#013b20\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6c5855c2980c1aa29cbfad1377c18aba\" style=\"color:#b00012\"><strong>Solve for&nbsp;<em>r<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-e5bea2e2c8058a9d8b8ada48083f4b94\" style=\"color:#b00012\">3(<em>r<\/em>&nbsp;+ 1)&nbsp;= 9<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-9dc95a36821abf628d1b3607f9513766\" style=\"color:#b00012\"><em>r<\/em>&nbsp;=&nbsp;&#8212;&#8212;-<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ef597f5f7343649aa45c222b4314f507\">Solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-4a646e1503fb8c85f8e3bb3f17628e1c\">3(<em>r<\/em>&nbsp;+ 1)&nbsp;=&nbsp;9<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e28fdac415ccc24d3acfd18f21be19e2\">3(<em>r<\/em>&nbsp;+ 1)\/3=9\/3     <em>Divide both sides by 3<\/em><br><em>r<\/em>&nbsp;+ 1&nbsp;=&nbsp;3                       <em>Simplify<\/em><br><em>r<\/em>&nbsp;+ 1 \u2212 1&nbsp;=&nbsp;3 \u2212 1     <em>Subtract 1 from both sides<\/em><br><em>r<\/em>&nbsp;=&nbsp;2                                                      <em>Simplify<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ee75b2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-708e3dd600767f5c34a9ef71bf77f8d3\" style=\"color:#b00012\"><strong>Solve for&nbsp;<em>m<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-96323c81c7098fde78e97b8d7a8333a4\" style=\"color:#b00012\">6 = 3(<em>m<\/em>&nbsp;\u2212 7)<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-ee16f36d5a00e9f744707d76fabeff1e\" style=\"color:#b00012\"><em>m<\/em>&nbsp;=&nbsp;&#8212;&#8211;<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ef597f5f7343649aa45c222b4314f507\">Solve.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-efbbbef300ac8afa3acad2cf2ee63d5b\">6&nbsp;=&nbsp;3(<em>m<\/em>&nbsp;\u2212 7)<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e62f68d74ec859db7caaf3c03d92fb67\">6\/3=3(m-7)\/3       <em>Divide both sides by 3<\/em><br>2&nbsp;=&nbsp;<em>m<\/em>&nbsp;\u2212 7               <em>Simplify<\/em><br>2 + 7&nbsp;=&nbsp;<em>m<\/em>&nbsp;\u2212 7 + 7     <em>Add 7 to both sides<\/em><br>9&nbsp;=&nbsp;<em>m                                     Simplify<\/em><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/95847\/741\/414\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-144.png\" alt=\"\" class=\"wp-image-8926\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-144.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-144-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-144-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/34069\/866\/829\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148.png\" alt=\"\" class=\"wp-image-8927\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve multi-step equations Class-8 Topic: Solve multi-step equations by Delta publications Key Notes: What Are Multi-Step Equations? Steps to Solve Multi-Step Equations Step 1: Simplify both sides Step 2: Move variable terms to one side Step 3: Move constant terms to the other side Step 4: Isolate the variable Step 5: Check your solution Example<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/w-8-solve-multi-step-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.8 Solve multi-step equations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-453","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/453","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=453"}],"version-history":[{"count":21,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/453\/revisions"}],"predecessor-version":[{"id":21255,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/453\/revisions\/21255"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}