{"id":31,"date":"2022-04-13T09:48:07","date_gmt":"2022-04-13T09:48:07","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=31"},"modified":"2025-07-31T09:43:40","modified_gmt":"2025-07-31T09:43:40","slug":"b-3-evaluate-variable-expressions-involving-integers","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/b-3-evaluate-variable-expressions-involving-integers\/","title":{"rendered":"B.3 Evaluate variable expressions involving integers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate variable expressions involving integers<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading\"><strong>Understanding Variable Expressions<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Definition:<\/strong>\n<ul class=\"wp-block-list\">\n<li>A variable expression (or algebraic expression) is a mathematical phrase that includes numbers, variables (letters representing unknown values), and operations.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Variables:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Variables are symbols (usually letters) that stand for unknown or changeable values.<\/li>\n\n\n\n<li>Example: In the expression 3x+4, x is the variable.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Evaluating Variable Expressions<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Substitution:<\/strong>\n<ul class=\"wp-block-list\">\n<li>To evaluate a variable expression, substitute the given value(s) of the variable(s) into the expression and perform the arithmetic operations.<\/li>\n\n\n\n<li>Example: Evaluate 3x+4 for x=2.\n<ul class=\"wp-block-list\">\n<li>Substitute x=: 3(2)+4<\/li>\n\n\n\n<li>Perform the operations: 6+4=10<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Order of Operations (PEMDAS):<\/strong>\n<ul class=\"wp-block-list\">\n<li>When evaluating expressions, always follow the order of operations:\n<ul class=\"wp-block-list\">\n<li><strong>P<\/strong>arentheses<\/li>\n\n\n\n<li><strong>E<\/strong>xponents (not typically covered in 6th grade, but good to be aware)<\/li>\n\n\n\n<li><strong>M<\/strong>ultiplication and <strong>D<\/strong>ivision (from left to right)<\/li>\n\n\n\n<li><strong>A<\/strong>ddition and <strong>S<\/strong>ubtraction (from left to right)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Steps to Evaluate Variable Expressions<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 1: Substitute the Values:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Replace the variables in the expression with their given values.<\/li>\n\n\n\n<li>Example: For x=3, y=4, evaluate 2x+3y.\n<ul class=\"wp-block-list\">\n<li>Substitute: 2(3)+3(4)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 2: Follow the Order of Operations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Perform any calculations inside parentheses first.<\/li>\n\n\n\n<li>Then, perform multiplication and division from left to right.<\/li>\n\n\n\n<li>Finally, perform addition and subtraction from left to right.<\/li>\n\n\n\n<li>Example: 2(3)+3(4)\n<ul class=\"wp-block-list\">\n<li>Multiply: 6+12<\/li>\n\n\n\n<li>Add: 18<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Examples<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Single Variable:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Evaluate 5x\u22127 for x=2\n<ul class=\"wp-block-list\">\n<li>Substitute: 5(2)\u22127)<\/li>\n\n\n\n<li>Calculate: 10\u22127=3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiple Variables:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Evaluate 3x+4y  for x=1 and y=2\n<ul class=\"wp-block-list\">\n<li>Substitute: 3(1)+4(2)<\/li>\n\n\n\n<li>Calculate: 3+8=11<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>With Parentheses:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Evaluate 2(x+y) for x=3 and y=5\n<ul class=\"wp-block-list\">\n<li>Substitute: 2(3+5)<\/li>\n\n\n\n<li>Calculate inside parentheses: 2(8)=16<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Tips for Students<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Substitute Carefully:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Ensure you replace each variable with the correct value.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Follow Order of Operations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Always use PEMDAS to avoid mistakes.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Show Your Work:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Write each step to make your calculations clear and to check for errors.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice Regularly:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Consistent practice with different types of expressions helps solidify understanding.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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:#90b8f1\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-4843ab7fc4d41d8c3dfd06967aee9837\" style=\"color:#b00012\">\ud83d\udd2e Evaluate the expression for&nbsp;<em>z<\/em>&nbsp;= 5.<\/p>\n\n\n\n<p>-3<em>z<\/em>&nbsp;=&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in z = 5 and simplify.<\/p>\n\n\n\n<p>-3z<\/p>\n\n\n\n<p>-3 (5)          Plug in z = 5<\/p>\n\n\n\n<p>-15            Multiply<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4a7ef\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-f2866f77c92a59541d35df568f80308d\" style=\"color:#b00012\">\ud83d\udd2e Evaluate the expression for&nbsp;<em>f<\/em>&nbsp;=&nbsp;-6.<\/p>\n\n\n\n<p>-2<em>f<\/em>&nbsp;+ 1 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in&nbsp;<em>f<\/em>&nbsp;=&nbsp;-6 and simplify.<\/p>\n\n\n\n<p>-2<em>f<\/em>&nbsp;+ 1 <\/p>\n\n\n\n<p>-2 (-6) + 1       Plugin f = \u20136<\/p>\n\n\n\n<p>12 + 1          Multiply<\/p>\n\n\n\n<p>13               Add<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f9aeae\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-066710dfce74b11dc12d2bcffc7e121e\" style=\"color:#b00012\">\ud83d\udd2eEvaluate the expression for&nbsp;<em>x<\/em>&nbsp;=&nbsp;-8.<\/p>\n\n\n\n<p><em>x<\/em>&nbsp;\u2212 8 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>Plug in&nbsp;<em>x<\/em>&nbsp;=&nbsp;-8 and simplify.<\/p>\n\n\n\n<p><em>x<\/em>&nbsp;\u2212 8 <\/p>\n\n\n\n<p>-8 &#8211; 8           Plug in x = \u20138<\/p>\n\n\n\n<p>-16            Subtract<\/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\/76091\/698\/849\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8.png\" alt=\"\" class=\"wp-image-6447\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-8-150x150.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\/76177\/531\/328\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8.png\" alt=\"\" class=\"wp-image-6448\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-8-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate variable expressions involving integers key notes: Understanding Variable Expressions Evaluating Variable Expressions Steps to Evaluate Variable Expressions Examples Tips for Students Learn with an example \ud83d\udd2e Evaluate the expression for&nbsp;z&nbsp;= 5. -3z&nbsp;=&nbsp; Plug in z = 5 and simplify. -3z -3 (5) Plug in z = 5 -15 Multiply \ud83d\udd2e Evaluate the expression for&nbsp;f&nbsp;=&nbsp;-6.<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/b-3-evaluate-variable-expressions-involving-integers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.3 Evaluate variable expressions involving integers&#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-31","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/31","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=31"}],"version-history":[{"count":20,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/31\/revisions"}],"predecessor-version":[{"id":18162,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/31\/revisions\/18162"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=31"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}