{"id":92,"date":"2022-04-12T09:31:57","date_gmt":"2022-04-12T09:31:57","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=92"},"modified":"2025-09-02T01:21:54","modified_gmt":"2025-09-02T01:21:54","slug":"e-9-multi-step-inequalities-with-decimals","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/e-9-multi-step-inequalities-with-decimals\/","title":{"rendered":"E.9 Multi-step inequalities with decimals"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multi-step inequalities with decimals<\/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\/DAGwfvYFeF4\/l6wRBPT_oxyJdpDmqRaSlA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwfvYFeF4&#x2F;l6wRBPT_oxyJdpDmqRaSlA&#x2F;watch?utm_content=DAGwfvYFeF4&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">7th E.9 Multi-Step Inequalities With Decimals<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/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>Understanding Inequalities<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">An inequality is a mathematical statement that shows the relationship between two expressions using symbols like <strong>&lt;<\/strong>, <strong>&gt;<\/strong>, <strong>\u2264<\/strong>, and <strong>\u2265<\/strong>.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Examples:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3.5 &gt; 2.1<\/strong> (3.5 is greater than 2.1)<\/li>\n\n\n\n<li><strong>x \u2264 4.6<\/strong> (x is less than or equal to 4.6)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Solving Multi-step Inequalities<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Multi-step inequalities involve more than one operation (addition, subtraction, multiplication, or division) to solve for the variable.<\/li>\n\n\n\n<li>The steps may include combining like terms, adding\/subtracting numbers, or dividing\/multiplying both sides of the inequality.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Steps to Solve Multi-step Inequalities with Decimals<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Step 1<\/strong>: Simplify both sides of the inequality if needed (combine like terms or distribute).<\/li>\n\n\n\n<li><strong>Step 2<\/strong>: Isolate the variable (get the variable on one side of the inequality).<\/li>\n\n\n\n<li><strong>Step 3<\/strong>: If necessary, perform operations like adding or subtracting decimals on both sides.<\/li>\n\n\n\n<li><strong>Step 4<\/strong>: If you multiply or divide by a negative number, <strong>flip the inequality sign<\/strong>.<\/li>\n\n\n\n<li><strong>Step 5<\/strong>: Solve for the variable and express the solution.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">4. <strong>Example 1<\/strong>: Solve the inequality:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>0.5x + 2.1 \u2265 4.6<\/strong>\n<ol class=\"wp-block-list\">\n<li>Subtract 2.1 from both sides:<br><strong>0.5x \u2265 2.5<\/strong><\/li>\n\n\n\n<li>Divide both sides by 0.5:<br><strong>x \u2265 5<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">5. <strong>Example 2<\/strong>: Solve the inequality:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>1.2x &#8211; 3.4 &lt; 5.6<\/strong>\n<ol class=\"wp-block-list\">\n<li>Add 3.4 to both sides:<br><strong>1.2x &lt; 9<\/strong><\/li>\n\n\n\n<li>Divide both sides by 1.2:<br><strong>x &lt; 7.5<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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 for Working with Decimals in Inequalities<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Convert decimals to fractions (if easier for you to work with) and then solve.<\/li>\n\n\n\n<li>Keep track of the decimal places during addition, subtraction, multiplication, and division.<\/li>\n\n\n\n<li>Use a calculator when necessary to ensure accuracy, especially for non-integer results.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Checking Your Solution<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>After solving, <strong>check your solution<\/strong> by substituting the value of the variable back into the original inequality to see if it satisfies the inequality.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Graphing Solutions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>After solving an inequality, you can represent the solution on a number line.<\/li>\n\n\n\n<li>Use an <strong>open circle<\/strong> for <strong>&lt;<\/strong> or <strong>&gt;<\/strong> and a <strong>closed circle<\/strong> for <strong>\u2264<\/strong> or <strong>\u2265<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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 Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>(a)<\/strong> Solve: <strong>2.5x + 3.2 \u2264 8.7<\/strong><\/li>\n\n\n\n<li><strong>(b)<\/strong> Solve: <strong>0.6x &#8211; 1.4 &gt; 3.5<\/strong><\/li>\n\n\n\n<li><strong>(c)<\/strong> Solve: <strong>4.8x + 2.1 \u2265 10.5<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-background-background-color has-text-color has-background has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-61565d4d27e48f84f82e6b0d44ab1e96\" style=\"background-color:#d8ffd1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-3682117c9a26b8a9d96fec5cc9c58cd8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f <strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">9.60 \u2212 0.96&nbsp;&nbsp;______  8.64<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify the left side.<\/p>\n\n\n\n<p>9.60 \u2212 0.96 _______ 8.64<\/p>\n\n\n\n<p>8.64 _____ 8.64<\/p>\n\n\n\n<p>Compare the numbers:<\/p>\n\n\n\n<p>8.64 = 8.64<\/p>\n\n\n\n<p>The = sign makes the statement true.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-7303a47b012eda50321c8237e3410e9e\" style=\"background-color:#fcc8f5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-bcb9eb1bda5e5a40a9ab7c667e0697c1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f<strong> Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">1.69&nbsp;______&nbsp;9.1 \u00f7 7<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify the right side. Remember to write the decimal point in the quotient.<\/p>\n\n\n\n<p>1.69&nbsp;____&nbsp;9.1 \u00f7 7<\/p>\n\n\n\n<p>1.69&nbsp;____&nbsp;1.3<\/p>\n\n\n\n<p>Compare the numbers.<\/p>\n\n\n\n<p>1.69 &gt; 1.3<\/p>\n\n\n\n<p>The &gt; sign makes the statement true.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-a15585a882fc9926a8aa8e70c90c1ad6\" style=\"background-color:#f3f9cd\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-927fd93a9f1200a63212beb68c90b1aa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\">\u25b6\ufe0f <strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">4.77 + 62.77&nbsp;____&nbsp;68.01<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify the left side.<\/p>\n\n\n\n<p>4.77 + 62.77 68.01<\/p>\n\n\n\n<p>67.54 68.01<\/p>\n\n\n\n<p>Compare the numbers:<\/p>\n\n\n\n<p>67.54 &lt; 68.01<\/p>\n\n\n\n<p>The &lt; sign makes the statement true.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/80639\/668\/812\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-249.png\" alt=\"\" class=\"wp-image-7333\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-249.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-249-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-249-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-249-400x400.png 400w\" 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\/84786\/431\/526\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-251.png\" alt=\"\" class=\"wp-image-7335\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-251.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-251-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-251-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-251-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multi-step inequalities with decimals 7th E.9 Multi-Step Inequalities With Decimals by Delta publications Key Notes: Understanding Inequalities An inequality is a mathematical statement that shows the relationship between two expressions using symbols like &lt;, &gt;, \u2264, and \u2265. Examples: Solving Multi-step Inequalities Steps to Solve Multi-step Inequalities with Decimals 4. Example 1: Solve the inequality:<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/e-9-multi-step-inequalities-with-decimals\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.9 Multi-step inequalities with decimals&#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,"footnotes":""},"class_list":["post-92","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Multi-step inequalities with decimals 7th E.9 Multi-Step Inequalities With Decimals by Delta publications Key Notes: An inequality is a mathematical statement that shows the relationship between two expressions using symbols like , \u2264, and \u2265. 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