{"id":4774,"date":"2017-12-27T00:26:04","date_gmt":"2017-12-27T00:26:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/?post_type=chapter&#038;p=4774"},"modified":"2018-01-03T15:57:31","modified_gmt":"2018-01-03T15:57:31","slug":"algebraic-expressions-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/chapter\/algebraic-expressions-review\/","title":{"raw":"Algebraic Expressions Review","rendered":"Algebraic Expressions Review"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Evaluating and simplifying algebraic expressions<\/li>\r\n \t<li>Expressions vs. equations<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2>Evaluate and Simplify Algebraic Expressions<\/h2>\r\nSo far, the mathematical expressions we have seen have involved real numbers only. In mathematics, we may see expressions such as [latex]x+5,\\frac{4}{3}\\pi {r}^{3}[\/latex], or [latex]-4x^2y^3[\/latex]. In the expression [latex]x+5[\/latex], 5 is called a <strong>constant<\/strong> because it does not vary and <em>x<\/em> is called a <strong>variable<\/strong> because it does. (In naming the variable, ignore any exponents or radicals containing the variable.) An <strong>algebraic expression<\/strong> is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division.\r\n\r\nWe have already seen some real number examples of exponential notation, a shorthand method of writing products of the same factor. When variables are used, the constants and variables are treated the same way.\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\left(-3\\right)^{5}=\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right) \\end{array}[\/latex]<\/div>\r\n<div><\/div>\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ } x^{5}=x\\cdot x\\cdot x\\cdot x\\cdot x\\end{array}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\left(2\\cdot7\\right)^{3}=\\left(2\\cdot7\\right)\\cdot\\left(2\\cdot7\\right)\\cdot\\left(2\\cdot7\\right) \\end{array}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ } \\left(yz\\right)^{3}=\\left(yz\\right)\\cdot\\left(yz\\right)\\cdot\\left(yz\\right)\\end{array}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\nIn each case, the exponent tells us how many factors of the base to use, whether the base consists of constants or variables.\r\n\r\nAny variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Describing Algebraic Expressions<\/h3>\r\nList the constants and variables for each algebraic expression.\r\n<ol>\r\n \t<li>[latex]x + 5[\/latex]<\/li>\r\n \t<li>[latex]\\frac{4}{3}\\pi {r}^{3}[\/latex]<\/li>\r\n \t<li>[latex]-4x^2y^3[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"790423\"]Solution[\/reveal-answer]\r\n[hidden-answer a=\"790423\"]\r\n<table summary=\"A table with four rows and three columns. The first entry of the first row is empty, but the second entry reads: Constants, and the third reads: Variables. The first entry of the second row reads: x plus five. The second column entry reads: five. The third column entry reads: x. The first entry of the third row reads: four-thirds pi times r cubed. The second column entry reads: four-thirds, pi. The third column entry reads: r. The first entry of the fourth row reads: the square root of two times m cubed times n squared. The second column entry reads: two. The third column entry reads: m, n.\">\r\n<thead>\r\n<tr>\r\n<th><\/th>\r\n<th>Constants<\/th>\r\n<th>Variables<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>1. <em>x<\/em> + 5<\/td>\r\n<td>5<\/td>\r\n<td><em>x<\/em><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2. [latex]\\frac{4}{3}\\pi {r}^{3}[\/latex]<\/td>\r\n<td>[latex]\\frac{4}{3},\\pi [\/latex]<\/td>\r\n<td>[latex]r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3. [latex]-4x^2y^3[\/latex]<\/td>\r\n<td>-4<\/td>\r\n<td>[latex]x,y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=109667&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"300\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Evaluating an Algebraic Expression at Different Values<\/h3>\r\nEvaluate the expression [latex]2x - 7[\/latex] for each value for <em>x.<\/em>\r\n<ol>\r\n \t<li>[latex]x=0[\/latex]<\/li>\r\n \t<li>[latex]x=1[\/latex]<\/li>\r\n \t<li>[latex]x=\\frac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]x=-4[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"421675\"]Solution[\/reveal-answer]\r\n[hidden-answer a=\"421675\"]\r\n<ol>\r\n \t<li>Substitute 0 for [latex]x[\/latex].\r\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill&amp; = 2\\left(0\\right)-7 \\\\ \\hfill&amp; =0-7 \\\\ \\hfill&amp; =-7\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute 1 for [latex]x[\/latex].\r\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill&amp; = 2\\left(1\\right)-7 \\\\ \\hfill&amp; =2-7 \\\\ \\hfill&amp; =-5\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute [latex]\\frac{1}{2}[\/latex] for [latex]x[\/latex].\r\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill&amp; = 2\\left(\\frac{1}{2}\\right)-7 \\\\ \\hfill&amp; =1-7 \\\\ \\hfill&amp; =-6\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute [latex]-4[\/latex] for [latex]x[\/latex].\r\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill&amp; = 2\\left(-4\\right)-7 \\\\ \\hfill&amp; =-8-7 \\\\ \\hfill&amp; =-15\\end{array}[\/latex]<\/div><\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div style=\"text-align: center\"><\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=1976&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"200\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Evaluating Algebraic Expressions<\/h3>\r\nEvaluate each expression for the given values.\r\n<ol>\r\n \t<li>[latex]x+5[\/latex] for [latex]x=-5[\/latex]<\/li>\r\n \t<li>[latex]\\frac{t}{2t - 1}[\/latex] for [latex]t=10[\/latex]<\/li>\r\n \t<li>[latex]\\frac{4}{3}\\pi {r}^{3}[\/latex] for [latex]r=5[\/latex]<\/li>\r\n \t<li>[latex]a+ab+b[\/latex] for [latex]a=11,b=-8[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"182854\"]Solution[\/reveal-answer]\r\n[hidden-answer a=\"182854\"]\r\n<ol>\r\n \t<li>Substitute [latex]-5[\/latex] for [latex]x[\/latex].\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }x+5\\hfill&amp;=\\left(-5\\right)+5 \\\\ \\hfill&amp;=0\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute 10 for [latex]t[\/latex].\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{t}{2t-1}\\hfill&amp; =\\frac{\\left(10\\right)}{2\\left(10\\right)-1} \\\\ \\hfill&amp; =\\frac{10}{20-1} \\\\ \\hfill&amp; =\\frac{10}{19}\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute 5 for [latex]r[\/latex].\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{4}{3}\\pi r^{3} \\hfill&amp; =\\frac{4}{3}\\pi\\left(5\\right)^{3} \\\\ \\hfill&amp; =\\frac{4}{3}\\pi\\left(125\\right) \\\\ \\hfill&amp; =\\frac{500}{3}\\pi\\end{array}[\/latex]<\/div><\/li>\r\n \t<li>Substitute 11 for [latex]a[\/latex] and \u20138 for [latex]b[\/latex].\r\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }a+ab+b \\hfill&amp; =\\left(11\\right)+\\left(11\\right)\\left(-8\\right)+\\left(-8\\right) \\\\ \\hfill&amp; =11-8-8 \\\\ \\hfill&amp; =-85\\end{array}[\/latex]<\/div><\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom10\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=483&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<iframe id=\"mom12\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=92388&amp;theme=oea&amp;iframe_resize_id=mom12\" width=\"100%\" height=\"200\"><\/iframe>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nIn the following video we present more examples of how to evaluate an expression for a given value.\r\n\r\nhttps:\/\/youtu.be\/MkRdwV4n91g\r\n<h2>Equations<\/h2>\r\nAn <strong>equation<\/strong> is a mathematical statement indicating that two expressions are equal. The expressions can be numerical or algebraic. The equation is not inherently true or false, but only a proposition. The values that make the equation true, the solutions, are found using the properties of real numbers and other results. For example, the equation [latex]2x+1=7[\/latex] has the unique solution [latex]x=3[\/latex] because when we substitute 3 for [latex]x[\/latex] in the equation, we obtain the true statement [latex]2\\left(3\\right)+1=7[\/latex].\r\n<div class=\"textbox tryit\">\r\n<h3>IS IT AN EXPRESSION OR AN EQUATION?<\/h3>\r\n[ohm_question]109934[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Evaluating and simplifying algebraic expressions<\/li>\n<li>Expressions vs. equations<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Evaluate and Simplify Algebraic Expressions<\/h2>\n<p>So far, the mathematical expressions we have seen have involved real numbers only. In mathematics, we may see expressions such as [latex]x+5,\\frac{4}{3}\\pi {r}^{3}[\/latex], or [latex]-4x^2y^3[\/latex]. In the expression [latex]x+5[\/latex], 5 is called a <strong>constant<\/strong> because it does not vary and <em>x<\/em> is called a <strong>variable<\/strong> because it does. (In naming the variable, ignore any exponents or radicals containing the variable.) An <strong>algebraic expression<\/strong> is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division.<\/p>\n<p>We have already seen some real number examples of exponential notation, a shorthand method of writing products of the same factor. When variables are used, the constants and variables are treated the same way.<\/p>\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\left(-3\\right)^{5}=\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right)\\cdot\\left(-3\\right) \\end{array}[\/latex]<\/div>\n<div><\/div>\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ } x^{5}=x\\cdot x\\cdot x\\cdot x\\cdot x\\end{array}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\left(2\\cdot7\\right)^{3}=\\left(2\\cdot7\\right)\\cdot\\left(2\\cdot7\\right)\\cdot\\left(2\\cdot7\\right) \\end{array}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ } \\left(yz\\right)^{3}=\\left(yz\\right)\\cdot\\left(yz\\right)\\cdot\\left(yz\\right)\\end{array}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<p>In each case, the exponent tells us how many factors of the base to use, whether the base consists of constants or variables.<\/p>\n<p>Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example: Describing Algebraic Expressions<\/h3>\n<p>List the constants and variables for each algebraic expression.<\/p>\n<ol>\n<li>[latex]x + 5[\/latex]<\/li>\n<li>[latex]\\frac{4}{3}\\pi {r}^{3}[\/latex]<\/li>\n<li>[latex]-4x^2y^3[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q790423\">Solution<\/span><\/p>\n<div id=\"q790423\" class=\"hidden-answer\" style=\"display: none\">\n<table summary=\"A table with four rows and three columns. The first entry of the first row is empty, but the second entry reads: Constants, and the third reads: Variables. The first entry of the second row reads: x plus five. The second column entry reads: five. The third column entry reads: x. The first entry of the third row reads: four-thirds pi times r cubed. The second column entry reads: four-thirds, pi. The third column entry reads: r. The first entry of the fourth row reads: the square root of two times m cubed times n squared. The second column entry reads: two. The third column entry reads: m, n.\">\n<thead>\n<tr>\n<th><\/th>\n<th>Constants<\/th>\n<th>Variables<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1. <em>x<\/em> + 5<\/td>\n<td>5<\/td>\n<td><em>x<\/em><\/td>\n<\/tr>\n<tr>\n<td>2. [latex]\\frac{4}{3}\\pi {r}^{3}[\/latex]<\/td>\n<td>[latex]\\frac{4}{3},\\pi[\/latex]<\/td>\n<td>[latex]r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>3. [latex]-4x^2y^3[\/latex]<\/td>\n<td>-4<\/td>\n<td>[latex]x,y[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=109667&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"300\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Evaluating an Algebraic Expression at Different Values<\/h3>\n<p>Evaluate the expression [latex]2x - 7[\/latex] for each value for <em>x.<\/em><\/p>\n<ol>\n<li>[latex]x=0[\/latex]<\/li>\n<li>[latex]x=1[\/latex]<\/li>\n<li>[latex]x=\\frac{1}{2}[\/latex]<\/li>\n<li>[latex]x=-4[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q421675\">Solution<\/span><\/p>\n<div id=\"q421675\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Substitute 0 for [latex]x[\/latex].\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill& = 2\\left(0\\right)-7 \\\\ \\hfill& =0-7 \\\\ \\hfill& =-7\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute 1 for [latex]x[\/latex].\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill& = 2\\left(1\\right)-7 \\\\ \\hfill& =2-7 \\\\ \\hfill& =-5\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute [latex]\\frac{1}{2}[\/latex] for [latex]x[\/latex].\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill& = 2\\left(\\frac{1}{2}\\right)-7 \\\\ \\hfill& =1-7 \\\\ \\hfill& =-6\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute [latex]-4[\/latex] for [latex]x[\/latex].\n<div>[latex]\\begin{array}\\text{ }2x-7 \\hfill& = 2\\left(-4\\right)-7 \\\\ \\hfill& =-8-7 \\\\ \\hfill& =-15\\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"text-align: center\"><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=1976&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"200\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Evaluating Algebraic Expressions<\/h3>\n<p>Evaluate each expression for the given values.<\/p>\n<ol>\n<li>[latex]x+5[\/latex] for [latex]x=-5[\/latex]<\/li>\n<li>[latex]\\frac{t}{2t - 1}[\/latex] for [latex]t=10[\/latex]<\/li>\n<li>[latex]\\frac{4}{3}\\pi {r}^{3}[\/latex] for [latex]r=5[\/latex]<\/li>\n<li>[latex]a+ab+b[\/latex] for [latex]a=11,b=-8[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q182854\">Solution<\/span><\/p>\n<div id=\"q182854\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Substitute [latex]-5[\/latex] for [latex]x[\/latex].\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }x+5\\hfill&=\\left(-5\\right)+5 \\\\ \\hfill&=0\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute 10 for [latex]t[\/latex].\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{t}{2t-1}\\hfill& =\\frac{\\left(10\\right)}{2\\left(10\\right)-1} \\\\ \\hfill& =\\frac{10}{20-1} \\\\ \\hfill& =\\frac{10}{19}\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute 5 for [latex]r[\/latex].\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }\\frac{4}{3}\\pi r^{3} \\hfill& =\\frac{4}{3}\\pi\\left(5\\right)^{3} \\\\ \\hfill& =\\frac{4}{3}\\pi\\left(125\\right) \\\\ \\hfill& =\\frac{500}{3}\\pi\\end{array}[\/latex]<\/div>\n<\/li>\n<li>Substitute 11 for [latex]a[\/latex] and \u20138 for [latex]b[\/latex].\n<div style=\"text-align: center\">[latex]\\begin{array}\\text{ }a+ab+b \\hfill& =\\left(11\\right)+\\left(11\\right)\\left(-8\\right)+\\left(-8\\right) \\\\ \\hfill& =11-8-8 \\\\ \\hfill& =-85\\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom10\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=483&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom12\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=92388&amp;theme=oea&amp;iframe_resize_id=mom12\" width=\"100%\" height=\"200\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p>In the following video we present more examples of how to evaluate an expression for a given value.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Evaluate Various Algebraic Expressions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/MkRdwV4n91g?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Equations<\/h2>\n<p>An <strong>equation<\/strong> is a mathematical statement indicating that two expressions are equal. The expressions can be numerical or algebraic. The equation is not inherently true or false, but only a proposition. The values that make the equation true, the solutions, are found using the properties of real numbers and other results. For example, the equation [latex]2x+1=7[\/latex] has the unique solution [latex]x=3[\/latex] because when we substitute 3 for [latex]x[\/latex] in the equation, we obtain the true statement [latex]2\\left(3\\right)+1=7[\/latex].<\/p>\n<div class=\"textbox tryit\">\n<h3>IS IT AN EXPRESSION OR AN EQUATION?<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm109934\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=109934&theme=oea&iframe_resize_id=ohm109934&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/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-4774\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation.. <strong>Provided 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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Evaluating Algebraic Expressions.. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/MkRdwV4n91g\">https:\/\/youtu.be\/MkRdwV4n91g<\/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>College Algebra.. <strong>Provided by<\/strong>: OpenStax College Algebra.. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/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 109934. <strong>Authored by<\/strong>: Mitchell,Nolan. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":60342,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Evaluating Algebraic Expressions.\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen 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