{"id":9239,"date":"2017-05-02T19:50:48","date_gmt":"2017-05-02T19:50:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9239"},"modified":"2017-08-14T17:55:44","modified_gmt":"2017-08-14T17:55:44","slug":"evaluating-algebraic-expressions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/evaluating-algebraic-expressions\/","title":{"raw":"Evaluating Algebraic Expressions","rendered":"Evaluating Algebraic Expressions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Evaluate an expression for a given value<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>\u00a0Evaluate Algebraic Expressions<\/h2>\r\nIn the last section, we simplified expressions using the order of operations. In this section, we\u2019ll evaluate expressions\u2014again following the order of operations.\r\n\r\nTo evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate [latex]x+7[\/latex] when\r\n<ol>\r\n \t<li>[latex]x=3[\/latex]<\/li>\r\n \t<li>[latex]x=12[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n\r\n1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n<table id=\"eip-id1166566546426\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7. Substitute 3 for x. The expression becomes 3 plus x which is 10.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute.<\/td>\r\n<td>[latex]\\color{red}{3}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].\r\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n<table id=\"eip-id1166566410105\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7, substitute 12 for x. The expression becomes 12 plus x which is 19.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute.<\/td>\r\n<td>[latex]\\color{red}{12}+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]19[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].\r\n\r\nNotice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[\/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144878[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate [latex]9x - 2,[\/latex] when\r\n<ol>\r\n \t<li>[latex]x=5[\/latex]<\/li>\r\n \t<li>[latex]x=1[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"711463\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"711463\"]\r\n\r\nSolution\r\nRemember [latex]ab[\/latex] means [latex]a[\/latex] times [latex]b[\/latex], so [latex]9x[\/latex] means [latex]9[\/latex] times [latex]x[\/latex].\r\n1. To evaluate the expression when [latex]x=5[\/latex], we substitute [latex]5[\/latex] for [latex]x[\/latex], and then simplify.\r\n<table id=\"eip-id1168469462966\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression nine x minus 2. Substitute 5 for x. The expression becomes 9 times 5 minus 2. Multiply first. Nine times 5 is 45 and the expression is now 45 minus 2. Subtract to get 43.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]9x-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{5}[\/latex] for x.<\/td>\r\n<td>[latex]9\\cdot\\color{red}{5}-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]45-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]43[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. To evaluate the expression when [latex]x=1[\/latex], we substitute [latex]1[\/latex] for [latex]x[\/latex], and then simplify.\r\n<table id=\"eip-id1168468440939\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression nine x minus 2. Substitute 1 for x. The expression becomes 9 times 1 minus 2. Multiply first. Nine times 1 is 9 and the expression is now 9 minus 2. Subtract to get 7.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]9x-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{1}[\/latex] for x.<\/td>\r\n<td>[latex]9(\\color{red}{1})-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]9-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in part 1 that we wrote [latex]9\\cdot 5[\/latex] and in part 2 we wrote [latex]9\\left(1\\right)[\/latex]. Both the dot and the parentheses tell us to multiply.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]141843[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate [latex]{x}^{2}[\/latex] when [latex]x=10[\/latex].\r\n[reveal-answer q=\"729694\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"729694\"]\r\n\r\nSolution\r\nWe substitute [latex]10[\/latex] for [latex]x[\/latex], and then simplify the expression.\r\n<table id=\"eip-id1168468538199\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x squared. Substitute 10 for x. The expression becomes 10 squared. By the definition of exponents, 10 squared is 10 times 10. Multiply to get 100.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x^2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x.<\/td>\r\n<td>[latex]{\\color{red}{10}}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of exponent.<\/td>\r\n<td>[latex]10\\cdot 10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]100[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=10[\/latex], the expression [latex]{x}^{2}[\/latex] has a value of [latex]100[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144879[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Evaluate }{2}^{x}\\text{ when }x=5[\/latex].\r\n[reveal-answer q=\"920379\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"920379\"]\r\n\r\nSolution\r\nIn this expression, the variable is an exponent.\r\n<table id=\"eip-id1168469574741\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression 2 to the power of x. Substitute 5 for x. The expression becomes 2 to the fifth power. By the definition of exponents, 2 to the fifth power is 2 times 2 times 2 times 2 times 2, or 5 factors of 2. Multiply from left to right to get 32.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2^x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{5}[\/latex] for x.<\/td>\r\n<td>[latex]{2}^{\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of exponent.<\/td>\r\n<td>[latex]2\\cdot2\\cdot2\\cdot2\\cdot2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=5[\/latex], the expression [latex]{2}^{x}[\/latex] has a value of [latex]32[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144882[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=10\\text{ and }y=2[\/latex].\r\n[reveal-answer q=\"769566\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"769566\"]\r\n\r\nSolution\r\n\r\n&nbsp;\r\n\r\nThis expression contains two variables, so we must make two substitutions.\r\n<table id=\"eip-id1168467158036\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3x+4y-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x and [latex]\\color{blue}{2}[\/latex] for y.<\/td>\r\n<td>[latex]3(\\color{red}{10})+4(\\color{blue}{2})-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]30+8-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add and subtract left to right.<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=10[\/latex] and [latex]y=2[\/latex], the expression [latex]3x+4y - 6[\/latex] has a value of [latex]32[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]144884[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Evaluate }2{x}^{2}+3x+8\\text{ when }x=4[\/latex].\r\n[reveal-answer q=\"971697\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"971697\"]\r\n\r\nSolution\r\nWe need to be careful when an expression has a variable with an exponent. In this expression, [latex]2{x}^{2}[\/latex] means [latex]2\\cdot x\\cdot x[\/latex] and is different from the expression [latex]{\\left(2x\\right)}^{2}[\/latex], which means [latex]2x\\cdot 2x[\/latex].\r\n<table id=\"eip-id1168466011069\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression two x squared plus three x plus 8. Substitute 4 for each x. The expression becomes 2 times 4 squared plus 3 times 4 plus 8. Simplify exponents first. Four squared is 16 so the expression becomes 2 times 16 plus 3 times 4 plus 8. Next perform multiplication from left to right. Two times 16 is 32 and 3 times 4 is 12. The expression becomes 32 plus 12 plus 8. Add from left to right. Thirty-two plus 12 is 44. Forty-four plus 8 is 52.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2x^2+3x+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{4}[\/latex] for each x.<\/td>\r\n<td>[latex]2{(\\color{red}{4})}^{2}+3(\\color{red}{4})+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify [latex]{4}^{2}[\/latex] .<\/td>\r\n<td>[latex]2(16)+3(4)+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]32+12+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]144886[\/ohm_question]\r\n\r\n<\/div>\r\nIn the video below we show more examples of how to substitute a value for variable in an expression, then evaluate the expression.\r\n\r\nhttps:\/\/youtu.be\/dkFIVfJTG9E","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate an expression for a given value<\/li>\n<\/ul>\n<\/div>\n<h2>\u00a0Evaluate Algebraic Expressions<\/h2>\n<p>In the last section, we simplified expressions using the order of operations. In this section, we\u2019ll evaluate expressions\u2014again following the order of operations.<\/p>\n<p>To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]x+7[\/latex] when<\/p>\n<ol>\n<li>[latex]x=3[\/latex]<\/li>\n<li>[latex]x=12[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<p>1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.<\/p>\n<table id=\"eip-id1166566546426\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7. Substitute 3 for x. The expression becomes 3 plus x which is 10.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td>[latex]\\color{red}{3}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]10[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].<br \/>\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.<\/p>\n<table id=\"eip-id1166566410105\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x plus 7, substitute 12 for x. The expression becomes 12 plus x which is 19.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td>[latex]\\color{red}{12}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]19[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].<\/p>\n<p>Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[\/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144878\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144878&theme=oea&iframe_resize_id=ohm144878&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]9x - 2,[\/latex] when<\/p>\n<ol>\n<li>[latex]x=5[\/latex]<\/li>\n<li>[latex]x=1[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q711463\">Show Solution<\/span><\/p>\n<div id=\"q711463\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nRemember [latex]ab[\/latex] means [latex]a[\/latex] times [latex]b[\/latex], so [latex]9x[\/latex] means [latex]9[\/latex] times [latex]x[\/latex].<br \/>\n1. To evaluate the expression when [latex]x=5[\/latex], we substitute [latex]5[\/latex] for [latex]x[\/latex], and then simplify.<\/p>\n<table id=\"eip-id1168469462966\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression nine x minus 2. Substitute 5 for x. The expression becomes 9 times 5 minus 2. Multiply first. Nine times 5 is 45 and the expression is now 45 minus 2. Subtract to get 43.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]9x-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{5}[\/latex] for x.<\/td>\n<td>[latex]9\\cdot\\color{red}{5}-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]45-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]43[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. To evaluate the expression when [latex]x=1[\/latex], we substitute [latex]1[\/latex] for [latex]x[\/latex], and then simplify.<\/p>\n<table id=\"eip-id1168468440939\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression nine x minus 2. Substitute 1 for x. The expression becomes 9 times 1 minus 2. Multiply first. Nine times 1 is 9 and the expression is now 9 minus 2. Subtract to get 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]9x-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{1}[\/latex] for x.<\/td>\n<td>[latex]9(\\color{red}{1})-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]9-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]7[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in part 1 that we wrote [latex]9\\cdot 5[\/latex] and in part 2 we wrote [latex]9\\left(1\\right)[\/latex]. Both the dot and the parentheses tell us to multiply.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141843\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141843&theme=oea&iframe_resize_id=ohm141843&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]{x}^{2}[\/latex] when [latex]x=10[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q729694\">Show Solution<\/span><\/p>\n<div id=\"q729694\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe substitute [latex]10[\/latex] for [latex]x[\/latex], and then simplify the expression.<\/p>\n<table id=\"eip-id1168468538199\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression x squared. Substitute 10 for x. The expression becomes 10 squared. By the definition of exponents, 10 squared is 10 times 10. Multiply to get 100.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x^2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x.<\/td>\n<td>[latex]{\\color{red}{10}}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td>[latex]10\\cdot 10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]100[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=10[\/latex], the expression [latex]{x}^{2}[\/latex] has a value of [latex]100[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144879\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144879&theme=oea&iframe_resize_id=ohm144879&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Evaluate }{2}^{x}\\text{ when }x=5[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q920379\">Show Solution<\/span><\/p>\n<div id=\"q920379\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nIn this expression, the variable is an exponent.<\/p>\n<table id=\"eip-id1168469574741\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression 2 to the power of x. Substitute 5 for x. The expression becomes 2 to the fifth power. By the definition of exponents, 2 to the fifth power is 2 times 2 times 2 times 2 times 2, or 5 factors of 2. Multiply from left to right to get 32.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2^x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{5}[\/latex] for x.<\/td>\n<td>[latex]{2}^{\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td>[latex]2\\cdot2\\cdot2\\cdot2\\cdot2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]32[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=5[\/latex], the expression [latex]{2}^{x}[\/latex] has a value of [latex]32[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144882\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144882&theme=oea&iframe_resize_id=ohm144882&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=10\\text{ and }y=2[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q769566\">Show Solution<\/span><\/p>\n<div id=\"q769566\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<p>&nbsp;<\/p>\n<p>This expression contains two variables, so we must make two substitutions.<\/p>\n<table id=\"eip-id1168467158036\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3x+4y-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{10}[\/latex] for x and [latex]\\color{blue}{2}[\/latex] for y.<\/td>\n<td>[latex]3(\\color{red}{10})+4(\\color{blue}{2})-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]30+8-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add and subtract left to right.<\/td>\n<td>[latex]32[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When [latex]x=10[\/latex] and [latex]y=2[\/latex], the expression [latex]3x+4y - 6[\/latex] has a value of [latex]32[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144884\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144884&theme=oea&iframe_resize_id=ohm144884&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Evaluate }2{x}^{2}+3x+8\\text{ when }x=4[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q971697\">Show Solution<\/span><\/p>\n<div id=\"q971697\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe need to be careful when an expression has a variable with an exponent. In this expression, [latex]2{x}^{2}[\/latex] means [latex]2\\cdot x\\cdot x[\/latex] and is different from the expression [latex]{\\left(2x\\right)}^{2}[\/latex], which means [latex]2x\\cdot 2x[\/latex].<\/p>\n<table id=\"eip-id1168466011069\" class=\"unnumbered unstyled\" summary=\"The image shows the given expression two x squared plus three x plus 8. Substitute 4 for each x. The expression becomes 2 times 4 squared plus 3 times 4 plus 8. Simplify exponents first. Four squared is 16 so the expression becomes 2 times 16 plus 3 times 4 plus 8. Next perform multiplication from left to right. Two times 16 is 32 and 3 times 4 is 12. The expression becomes 32 plus 12 plus 8. Add from left to right. Thirty-two plus 12 is 44. Forty-four plus 8 is 52.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2x^2+3x+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{4}[\/latex] for each x.<\/td>\n<td>[latex]2{(\\color{red}{4})}^{2}+3(\\color{red}{4})+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify [latex]{4}^{2}[\/latex] .<\/td>\n<td>[latex]2(16)+3(4)+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]32+12+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]52[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144886\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144886&theme=oea&iframe_resize_id=ohm144886&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the video below we show more examples of how to substitute a value for variable in an expression, then evaluate the expression.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Substitute and Evaluate  Expressions x^2+3, (x+3)^2, x^2+2x+3\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/dkFIVfJTG9E?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9239\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Substitute and Evaluate Expressions x^2+3, (x+3)^2, x^2+2x+3. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/dkFIVfJTG9E\">https:\/\/youtu.be\/dkFIVfJTG9E<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 144878, 141843, 144879, 144882, 144884, 144886. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Substitute and Evaluate Expressions x^2+3, (x+3)^2, x^2+2x+3\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/dkFIVfJTG9E\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Question ID: 144878, 141843, 144879, 144882, 144884, 144886\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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