{"id":240,"date":"2022-04-13T08:48:19","date_gmt":"2022-04-13T08:48:19","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=240"},"modified":"2025-04-09T09:11:13","modified_gmt":"2025-04-09T09:11:13","slug":"n-7-solve-equations-complete-the-solution","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/n-7-solve-equations-complete-the-solution\/","title":{"rendered":"N.7 Solve equations: complete the solution"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Solve equations: complete the solution<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-28d136ae4331e7eb05ec8e1cb71ebcde\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-5f38cfa4d04c7b01d36ebe7443ecf638\" style=\"color:#000060\"><strong>Understanding the Equation<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>An <strong>equation<\/strong> is a statement that two expressions are equal.<\/li>\n\n\n\n<li>It often contains a variable (e.g., <em>x<\/em>) that you need to solve for.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-9c597280c033f8f2220813eeec1710af\" style=\"color:#000060\"><strong>Goal of Solving an Equation<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Find the <strong>value of the variable<\/strong> that makes the equation <strong>true<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-4511b29cae1190fe063ec766e87fa284\" style=\"color:#000060\"><strong>Types of Equations<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>One-step equations<\/strong> (e.g., x + 5 = 9)<\/li>\n\n\n\n<li><strong>Two-step equations<\/strong> (e.g., 2x &#8211; 3 = 7)<\/li>\n\n\n\n<li><strong>Multi-step equations<\/strong> (e.g., 3x + 2 = 2x + 7)<\/li>\n\n\n\n<li><strong>Equations with variables on both sides<\/strong><\/li>\n\n\n\n<li><strong>Equations with brackets or fractions<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-9105bf259489e20dce213a3146e0490c\" style=\"color:#000060\"><strong>Basic Steps to Solve Equations<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Simplify<\/strong> both sides (remove brackets, combine like terms).<\/li>\n\n\n\n<li><strong>Move variable terms<\/strong> to one side and constant terms to the other.<\/li>\n\n\n\n<li><strong>Isolate the variable<\/strong> using inverse operations (add, subtract, multiply, divide).<\/li>\n\n\n\n<li><strong>Solve<\/strong> for the variable.<\/li>\n\n\n\n<li><strong>Check your solution<\/strong> by substituting back into the original equation.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-e12bd5e0de19bd02e40dfc07b18477ab\" style=\"color:#000060\"><strong>Inverse Operations<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Used to &#8220;undo&#8221; operations:<\/p>\n\n\n\n<p class=\"has-large-font-size\">Addition \u2194 Subtraction<\/p>\n\n\n\n<p class=\"has-large-font-size\">Multiplication \u2194 Division<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-b719788c88f8ef94f984cc435d670ade\" style=\"color:#000060\"><strong>Keeping the Equation Balanced<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Whatever you do to <strong>one side<\/strong>, you must do to the <strong>other side<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-ffa3774ee92fe25d1d875dfbcafe71b1\" style=\"color:#000060\"><strong>Common Mistakes to Avoid<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Forgetting to apply operations to <strong>both sides<\/strong><\/li>\n\n\n\n<li>Sign errors (positive\/negative)<\/li>\n\n\n\n<li>Not simplifying expressions fully<\/li>\n\n\n\n<li>Not checking your final answer<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-48d2e6dec9471e99d52b9e1faf56f2c8\" style=\"color:#000060\"><strong>Special Cases<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>No solution<\/strong>: Both sides can&#8217;t be equal (e.g., x + 2 = x + 5)<\/li>\n\n\n\n<li><strong>Infinite solutions<\/strong>: Both sides are exactly the same (e.g., 2x + 1 = 2x + 1)<\/li>\n<\/ul>\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-large-font-size\" style=\"background-color:#afc0ea\"><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>Complete&nbsp;the process of solving the&nbsp;equation.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Fill&nbsp;in the missing term on each line. Simplify any&nbsp;fractions.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>5(x + 2) = 10<\/td><td><\/td><\/tr><tr><td>x +2 = ______<\/td><td>Divide both sides by 5<\/td><\/tr><tr><td>x = ____<\/td><td>Subtract 2 from both sides<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;complete the process of solving the equation, understand what changes from one line to the&nbsp;next.<\/p>\n\n\n\n<p>Start&nbsp;at the top with the first and second&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>5(x + 2) = 10<\/td><td>\ufeff<\/td><\/tr><tr><td>x +2 = ______<\/td><td>Divide both sides by 5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, divide both sides of the equation by&nbsp;5.<\/p>\n\n\n\n<p>5(x+2) = 10<\/p>\n\n\n\n<p>5(x+2)\/<strong>5<\/strong> = 10\/<strong>5<\/strong><\/p>\n\n\n\n<p>x+2 = 2<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>2<\/strong>.<\/p>\n\n\n\n<p>Look&nbsp;at the second and third&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x +2 = ______<\/td><td><\/td><\/tr><tr><td>x = ____<\/td><td>Subtract 2 from both sides<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, subtract&nbsp;2&nbsp;from both sides of the&nbsp;equation.<\/p>\n\n\n\n<p>x+2 = 2<\/p>\n\n\n\n<p>x+2\u2013<strong>2<\/strong> = 2\u2013<strong>2<\/strong><\/p>\n\n\n\n<p>x = 0<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>0<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b7eaae\"><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>Complete&nbsp;the process of solving the&nbsp;equation.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Fill&nbsp;in the missing term on each line. Simplify any&nbsp;fractions.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>3(w +4) = 18<\/td><td><\/td><\/tr><tr><td>w + 4 =_______<\/td><td>Divide both sides by 3<\/td><\/tr><tr><td>w = ______<\/td><td>Subtract 4 from both sides<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;complete the process of solving the equation, understand what changes from one line to the&nbsp;next.<\/p>\n\n\n\n<p>Start&nbsp;at the top with the first and second&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>3(w +4) = 18<\/td><td>\ufeff<\/td><\/tr><tr><td>w + 4 =_______<\/td><td>Divide both sides by 3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, divide both sides of the equation by&nbsp;3.<\/p>\n\n\n\n<p>3(w+4) = 18<\/p>\n\n\n\n<p>3(w+4)<strong>3<\/strong> = 18\/<strong>3<\/strong><\/p>\n\n\n\n<p>w+4 = 6<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>6<\/strong>.<\/p>\n\n\n\n<p>Look&nbsp;at the second and third&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>w + 4 = 6<\/td><td><\/td><\/tr><tr><td>w = ______<\/td><td>Subtract 4 from both sides<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, subtract&nbsp;4&nbsp;from both sides of the&nbsp;equation.<\/p>\n\n\n\n<p>w+4 = 6<\/p>\n\n\n\n<p>w+4\u2013<strong>4<\/strong> = 6\u2013<strong>4<\/strong><\/p>\n\n\n\n<p>w = 2<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>2<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ea9cf1\"><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>Complete&nbsp;the process of solving the&nbsp;equation.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Fill&nbsp;in the missing term on each line. Simplify any&nbsp;fractions.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>9y + 19 = 19<\/td><td><\/td><\/tr><tr><td>9y = _______<\/td><td>Subtract 19 from both sides<\/td><\/tr><tr><td>y = _____<\/td><td>Divide both sides by 9<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;complete the process of solving the equation, understand what changes from one line to the&nbsp;next.<\/p>\n\n\n\n<p>Start&nbsp;at the top with the first and second&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>9y + 19 = 19<\/td><td>\ufeff<\/td><\/tr><tr><td>9y = _______<\/td><td>Subtract 19 from both sides<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, subtract&nbsp;19&nbsp;from both sides of the&nbsp;equation.<\/p>\n\n\n\n<p>9y+19 = 19<\/p>\n\n\n\n<p>9y+19\u2013<strong>19<\/strong> = 19\u2013<strong>19<\/strong><\/p>\n\n\n\n<p>9y = 0<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>0<\/strong>.<\/p>\n\n\n\n<p>Look&nbsp;at the second and third&nbsp;lines.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>9y = 0<\/td><td><\/td><\/tr><tr><td>y = ______<\/td><td>Divide both sides by 9<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>To&nbsp;find the missing term, divide both sides of the equation by&nbsp;9.<\/p>\n\n\n\n<p>9y = 0<\/p>\n\n\n\n<p>9y \/ <strong>9<\/strong> = 0 \/ <strong>9<\/strong><\/p>\n\n\n\n<p>y = 0<\/p>\n\n\n\n<p>The&nbsp;missing term is&nbsp;<strong>0<\/strong>.<\/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\/90144\/368\/583\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-82.png\" alt=\"\" class=\"wp-image-7936\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-82.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-82-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-82-150x150.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\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-91.png\" alt=\"\" class=\"wp-image-7937\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-91.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-91-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-91-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve equations: complete the solution key notes : Understanding the Equation Goal of Solving an Equation Types of Equations Basic Steps to Solve Equations Inverse Operations Used to &#8220;undo&#8221; operations: Addition \u2194 Subtraction Multiplication \u2194 Division Keeping the Equation Balanced Common Mistakes to Avoid Special Cases Learn with an example Complete&nbsp;the process of solving the&nbsp;equation.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/n-7-solve-equations-complete-the-solution\/\">Continue reading <span class=\"screen-reader-text\">&#8220;N.7 Solve equations: complete the solution&#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-240","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240\/revisions"}],"predecessor-version":[{"id":16694,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240\/revisions\/16694"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}