{"id":151,"date":"2020-08-21T19:43:03","date_gmt":"2020-08-21T23:43:03","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/evaluate-simplify-and-translate-expressions\/"},"modified":"2021-03-24T10:51:45","modified_gmt":"2021-03-24T14:51:45","slug":"evaluate-simplify-and-translate-expressions","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/evaluate-simplify-and-translate-expressions\/","title":{"raw":"1.3 Evaluate, Simplify, and Translate Expressions","rendered":"1.3 Evaluate, Simplify, and Translate Expressions"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Evaluate algebraic expressions<\/li>\n \t<li>Identify terms, coefficients, and like terms<\/li>\n \t<li>Simplify expressions by combining like terms<\/li>\n \t<li>Translate word phrases to algebraic expressions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Evaluate Algebraic Expressions<\/h1>\n<p id=\"fs-id2907739\">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 id=\"fs-id1632121\">To evaluate an algebraic expression means to find the value of the expression when the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> is replaced by a given number. To evaluate an <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1372248\" data-type=\"problem\">\n<p id=\"fs-id1987806\">Evaluate \\(x+7\\) when<\/p>\n\n<ol id=\"eip-id1168467157803\" class=\"circled\" type=\"a\">\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=3\\)<\/li>\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=12\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2388055\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1576712\">a. To evaluate, substitute \\(3\\) for \\(x\\) in the expression, and then simplify.<\/p>\n\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><span id=\"eip-id1166566546450\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td><span id=\"eip-id1166566546467\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1166566311657\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2650628\">When \\(x=3\\), the expression \\(x+7\\) has a value of \\(10\\).<\/p>\n<p id=\"fs-id2819088\">b. To evaluate, substitute \\(12\\) for \\(x\\) in the expression, and then simplify.<\/p>\n\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><span id=\"eip-id1166566434247\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMAth_Figure_02_02_008_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td><span id=\"eip-id1166566434264\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_008_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1166566434281\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_008_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1737222\">When \\(x=12\\), the expression \\(x+7\\) has a value of \\(19\\).<\/p>\n<p id=\"fs-id1736700\">Notice that we got different results for parts a) and b) even though we started with the same expression. This is because the values used for \\(x\\) were different. When we evaluate an expression, the value varies depending on the value used for the variable.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2211298\" data-type=\"problem\">\n<p id=\"fs-id1357478\">Evaluate:<\/p>\n<p id=\"fs-id1800084\">\\(y+4\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\n\n<ol id=\"eip-id1168467133964\" class=\"circled\" type=\"a\">\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}y=6\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}y=15\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1946698\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468303825\" class=\"circled\" type=\"a\">\n \t<li>\u00a010<\/li>\n \t<li>\u00a019<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1893299\" data-type=\"problem\">\n<p id=\"fs-id1171105480166\">Evaluate:<\/p>\n<p id=\"fs-id2138650\">\\(a-5\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\n\n<ol id=\"eip-id1168469871235\" class=\"circled\" type=\"a\">\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}a=9\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}a=17\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id3293034\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468555320\" class=\"circled\" type=\"a\">\n \t<li>\u00a04<\/li>\n \t<li>\u00a012<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2603896\" data-type=\"problem\">\n<p id=\"fs-id1800944\">Evaluate \\(9x-2,\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\n\n<ol id=\"eip-id1168468470077\" class=\"circled\" type=\"a\">\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=5\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=1\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1406199\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2311961\">Remember \\(ab\\) means \\(a\\) times \\(b\\), so \\(9x\\) means \\(9\\) times \\(x\\).<\/p>\n<p id=\"fs-id3177480\">a. To evaluate the expression when \\(x=5\\), we substitute \\(5\\) for \\(x\\), and then simplify.<\/p>\n\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><span id=\"eip-id1168469462986\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469463000\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168469463011\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469463028\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168469463045\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2440233\">b. To evaluate the expression when \\(x=1\\), we substitute \\(1\\) for \\(x\\), and then simplify.<\/p>\n\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><span id=\"eip-id1168468440960\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468440974\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168468440984\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468441002\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168468441019\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2216151\">Notice that in part a) that we wrote \\(9\\cdot 5\\) and in part b) we wrote \\(9\\left(1\\right)\\). Both the dot and the parentheses tell us to multiply.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1368058\" data-type=\"problem\">\n<p id=\"fs-id2451489\">Evaluate:<\/p>\n<p id=\"fs-id2136380\">\\(8x-3,\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\n\n<ol id=\"eip-id1168469756827\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x=2\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x=1\\)<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467257646\" class=\"circled\" type=\"a\">\n \t<li>\u00a013<\/li>\n \t<li>\u00a05<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2761352\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1370240\" data-type=\"exercise\">\n<div id=\"fs-id1368058\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2420879\" data-type=\"problem\">\n<p id=\"fs-id1171105140307\">Evaluate:<\/p>\n<p id=\"fs-id1281318\">\\(4y-4,\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\n\n<ol id=\"eip-id1168466004460\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y=3\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y=5\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2439809\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468610088\" class=\"circled\" type=\"a\">\n \t<li>\u00a08<\/li>\n \t<li>\u00a016<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103512900\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1792161\" data-type=\"exercise\">\n<div id=\"fs-id2420879\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2756986\" data-type=\"problem\">\n<p id=\"fs-id1811335\">Evaluate \\({x}^{2}\\) when \\(x=10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2661268\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2214943\">We substitute \\(10\\) for \\(x\\), and then simplify the expression.<\/p>\n\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><span id=\"eip-id1168468538220\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468538234\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168468538245\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168468538262\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468538279\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2197016\">When \\(x=10\\), the expression \\({x}^{2}\\) has a value of \\(100\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1881940\" data-type=\"problem\">\n<p id=\"fs-id1283634\">Evaluate:<\/p>\n<p id=\"fs-id1498924\">\\({x}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2296111\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1806491\">64<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1498997\" data-type=\"problem\">\n<p id=\"fs-id1171105158454\">Evaluate:<\/p>\n<p id=\"fs-id1546580\">\\({x}^{3}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2201260\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1180287\">216<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1863809\" data-type=\"problem\">\n<p id=\"fs-id1325186\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}{2}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=5\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2784321\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1731877\">In this expression, the variable is an exponent.<\/p>\n\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><span id=\"eip-id1168469574762\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469574776\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168469574787\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168469574804\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469574821\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1547737\">When \\(x=5\\), the expression \\({2}^{x}\\) has a value of \\(32\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105339525\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id902234\" data-type=\"exercise\">\n<div id=\"fs-id2201260\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<p id=\"fs-id2630090\">Evaluate:<\/p>\n<p id=\"fs-id2130634\">\\({2}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2136192\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1824352\">64<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105139468\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1346408\" data-type=\"exercise\">\n<div id=\"fs-id4363755\" data-type=\"problem\">\n<p id=\"fs-id1171105090102\"><\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nEvaluate:\n<div id=\"fs-id4363755\" data-type=\"problem\">\n<p id=\"fs-id2657794\">\\({3}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2691459\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2326737\">81<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1891867\" data-type=\"problem\">\n<p id=\"fs-id2276108\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}3x+4y-6\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=10\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}y=2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2439822\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2264342\">This expression contains two variables, so we must make two substitutions.<\/p>\n\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><span id=\"eip-id1168467237223\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168467237237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168467237247\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168467237264\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add and subtract left to right.<\/td>\n<td><span id=\"eip-id1168467237280\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1470900\">When \\(x=10\\) and \\(y=2\\), the expression \\(3x+4y-6\\) has a value of \\(32\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<p id=\"fs-id2267372\">Evaluate:<\/p>\n<p id=\"fs-id1160292\">\\(2x+5y-4\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=11\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}y=3\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1630119\" data-type=\"solution\"><details><summary>Show Answer<\/summary>33\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1603080\" data-type=\"problem\">\n<p id=\"fs-id1171105115923\">Evaluate:<\/p>\n<p id=\"fs-id1718253\">\\(5x-2y-9\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=7\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}y=8\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1494384\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2555520\">10<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1369028\" data-type=\"exercise\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1785986\" data-type=\"problem\">\n<p id=\"fs-id2657506\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}2{x}^{2}+3x+8\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1383958\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2310003\">We need to be careful when an expression has a variable with an exponent. In this expression, \\(2{x}^{2}\\) means \\(2\\cdot x\\cdot x\\) and is different from the expression \\({\\left(2x\\right)}^{2}\\), which means \\(2x\\cdot 2x\\).<\/p>\n\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><span id=\"eip-id1168466011092\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466011106\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1168466011116\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify \\({4}^{2}\\).<\/td>\n<td><span id=\"eip-id1168466011141\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168466011158\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1168466011175\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2454530\" data-type=\"problem\">\n<p id=\"fs-id2646106\">Evaluate:<\/p>\n<p id=\"fs-id2265086\">\\(3{x}^{2}+4x+1\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2835764\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1299685\">40<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1259006\" data-type=\"problem\">\n<p id=\"fs-id1171105115753\">Evaluate:<\/p>\n<p id=\"fs-id1605750\">\\(6{x}^{2}-4x-7\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2466793\" data-type=\"solution\"><details><summary>Show Answer<\/summary>9\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Identify Terms, Coefficients, and Like Terms<\/h1>\n<p id=\"fs-id2487968\">Algebraic expressions are made up of <em data-effect=\"italics\">terms<\/em>. A term is a constant or the product of a constant and one or more variables. Some examples of terms are \\(7,y,5{x}^{2},9a,\\text{and}\\phantom{\\rule{0.2em}{0ex}}13xy\\).<\/p>\n<p id=\"fs-id1965867\">The constant that multiplies the variable(s) in a term is called the coefficient. We can think of the coefficient as the number <em data-effect=\"italics\">in front of<\/em> the variable. The coefficient of the term \\(3x\\) is \\(3\\). When we write \\(x\\), the coefficient is \\(1\\), since \\(x=1\\cdot x\\). The table below gives the coefficients for each of the terms in the left column.<\/p>\n\n<table id=\"fs-id2266631\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cTerm\u201d and the second \u201cCoefficient\u201d. The next row has the number 7 in the \u201cTerm\u201d column and the number 7 in the \u201cCoefficient\u201d column. The next row has the term 9 a in the \u201cTerm\u201d column and the number 9 in the \u201cCoefficient\u201d column. The next row has the letter y in the \u201cTerm\u201d column and the number 1 in the \u201cCoefficient\u201d column. The last row has the term 5 x squared in the \u201cTerm\u201d column and the number 5 in the \u201cCoefficient\u201d column.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\">Term<\/th>\n<th scope=\"col\" data-align=\"center\">Coefficient<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\">\\(7\\)<\/td>\n<td data-align=\"left\">\\(7\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">\\(9a\\)<\/td>\n<td data-align=\"left\">\\(9\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">\\(y\\)<\/td>\n<td data-align=\"left\">\\(1\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">\\(5{x}^{2}\\)<\/td>\n<td data-align=\"left\">\\(5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id3011311\">An algebraic expression may consist of one or more terms added or subtracted. In this chapter, we will only work with terms that are added together. The table below gives some examples of algebraic expressions with various numbers of terms. Notice that we include the operation before a term with it.<\/p>\n\n<table id=\"fs-id1596496\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d and the second \u201cTerms\u201d. The next row has the number 7 in the \u201cExpression\u201d column and the number 7 in the \u201cTerms\u201d column. The next row has the letter y in the \u201cExpression\u201d column and the letter y in the \u201cTerms\u201d column. The next row has the expression x plus 7 in the \u201cExpression\u201d column and the letter x and the number 7 listed in the \u201cTerms\u201d column. The next row has the expression 2 x plus 7 y plus 4 in the \u201cExpression\u201d column and the terms 2 x, 7 y, and 4 listed in the \u201cTerms\u201d column. The last row has the expression 3 x squared plus 4 x squared plus 5 y plus 3 in the \u201cExpression\u201d column and the terms 3 x squared, 4 x squared, 5 y and 3 listed in the \u201cTerms\u201d column.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\">Expression<\/th>\n<th scope=\"col\" data-align=\"center\">Terms<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(7\\)<\/td>\n<td data-align=\"left\">\\(7\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(y\\)<\/td>\n<td data-align=\"left\">\\(y\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(x+7\\)<\/td>\n<td data-align=\"left\">\\(x,7\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(2x+7y+4\\)<\/td>\n<td data-align=\"left\">\\(2x,7y,4\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(3{x}^{2}+4{x}^{2}+5y+3\\)<\/td>\n<td data-align=\"left\">\\(3{x}^{2},4{x}^{2},5y,3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1919072\" data-type=\"problem\">\n<p id=\"fs-id1512228\">Identify each term in the expression \\(9b+15{x}^{2}+a+6\\). Then identify the coefficient of each term.<\/p>\n\n<\/div>\n<div id=\"fs-id1823248\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2581602\">The expression has four terms. They are \\(9b,15{x}^{2},a\\), and \\(6\\).<\/p>\n<p id=\"fs-id1405969\">The coefficient of \\(9b\\) is \\(9\\).<\/p>\n<p id=\"fs-id2593979\">The coefficient of \\(15{x}^{2}\\) is \\(15\\).<\/p>\n<p id=\"fs-id1944608\">Remember that if no number is written before a variable, the coefficient is \\(1\\). So the coefficient of \\(a\\) is \\(1\\).<\/p>\n<p id=\"fs-id2265026\">The coefficient of a constant is the constant, so the coefficient of \\(6\\) is \\(6\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2281474\" data-type=\"problem\">\n<p id=\"fs-id1620052\">Identify all terms in the given expression, and their coefficients:<\/p>\n<p id=\"fs-id2307665\">\\(4x+3b+2\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1534340\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2786022\">The terms are 4<em data-effect=\"italics\">x<\/em>, 3<em data-effect=\"italics\">b<\/em>, and 2. The coefficients are 4, 3, and 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1171103838018\">Identify all terms in the given expression, and their coefficients:<\/p>\n<p id=\"fs-id1335442\">\\(9a+13{a}^{2}+{a}^{3}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1575179\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id883422\">The terms are 9<em data-effect=\"italics\">a<\/em>, 13<em data-effect=\"italics\">a<\/em><sup>2<\/sup>, and <em data-effect=\"italics\">a<\/em><sup>3<\/sup>, The coefficients are 9, 13, and 1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nSome terms share common traits. Look at the following terms. Which ones seem to have traits in common?\n\n\\(5x,7,{n}^{2},4,3x,9{n}^{2}\\)\n\n<\/div>\n<p id=\"fs-id1283119\">Which of these terms are like terms?<\/p>\n\n<ul id=\"fs-id1627987\" data-bullet-style=\"bullet\">\n \t<li>The terms \\(7\\) and \\(4\\) are both constant terms.<\/li>\n \t<li>The terms \\(5x\\) and \\(3x\\) are both terms with \\(x\\).<\/li>\n \t<li>The terms \\({n}^{2}\\) and \\(9{n}^{2}\\) both have \\({n}^{2}\\).<\/li>\n<\/ul>\n<p id=\"fs-id1372814\">Terms are called like terms if they have the same variables and exponents. All constant terms are also like terms. So among the terms \\(5x,7,{n}^{2},4,3x,9{n}^{2}\\),<\/p>\n\n<div id=\"fs-id2268628\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(7\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}4\\phantom{\\rule{0.2em}{0ex}}\\text{are like terms.}\\)<\/div>\n<div id=\"fs-id555738\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(5x\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}3x\\phantom{\\rule{0.2em}{0ex}}\\text{are like terms.}\\)<\/div>\n<div id=\"fs-id2662299\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({n}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}9{n}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{are like terms.}\\)<\/div>\n<div id=\"fs-id2129414\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Like Terms<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nTerms that are either constants or have the same variables with the same exponents are like terms.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n\nIdentify the like terms:\n<ol id=\"eip-id1168468588896\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{y}^{3},7{x}^{2},14,23,4{y}^{3},9x,5{x}^{2}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}4{x}^{2}+2x+5{x}^{2}+6x+40x+8xy\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2142618\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1190825\">a. \\(\\phantom{\\rule{0.2em}{0ex}}{y}^{3},7{x}^{2},14,23,4{y}^{3},9x,5{x}^{2}\\)<\/p>\n<p id=\"fs-id1335628\">Look at the variables and exponents. The expression contains \\({y}^{3},{x}^{2},x\\), and constants.<\/p>\n<p id=\"fs-id1587743\">The terms \\({y}^{3}\\) and \\(4{y}^{3}\\) are like terms because they both have \\({y}^{3}\\).<\/p>\n<p id=\"fs-id1408738\">The terms \\(7{x}^{2}\\) and \\(5{x}^{2}\\) are like terms because they both have \\({x}^{2}\\).<\/p>\n<p id=\"fs-id1531249\">The terms \\(14\\) and \\(23\\) are like terms because they are both constants.<\/p>\nThe term \\(9x\\) does not have any like terms in this list since no other terms have the variable \\(x\\) raised to the power of \\(1\\).\n<p id=\"fs-id2649666\">b. \\(\\phantom{\\rule{0.2em}{0ex}}4{x}^{2}+2x+5{x}^{2}+6x+40x+8xy\\)<\/p>\n<p id=\"fs-id2495896\">Look at the variables and exponents. The expression contains the terms \\(4{x}^{2},2x,5{x}^{2},6x,40x,\\text{and}\\phantom{\\rule{0.2em}{0ex}}8xy\\)<\/p>\n<p id=\"fs-id1462544\">The terms \\(4{x}^{2}\\) and \\(5{x}^{2}\\) are like terms because they both have \\({x}^{2}\\).<\/p>\n<p id=\"fs-id1194075\">The terms \\(2x,6x,\\text{and}\\phantom{\\rule{0.2em}{0ex}}40x\\) are like terms because they all have \\(x\\).<\/p>\n<p id=\"fs-id2173435\">The term \\(8xy\\) has no like terms in the given expression because no other terms contain the two variables \\(xy\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1581991\">Identify the like terms in the list or the expression:<\/p>\n<p id=\"fs-id1335600\">\\(9,2{x}^{3},{y}^{2},8{x}^{3},15,9y,11{y}^{2}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1886900\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2481939\">9, 15; 2<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 8<em data-effect=\"italics\">x<\/em><sup>3<\/sup>, <em data-effect=\"italics\">y<\/em><sup>2<\/sup>, and 11<em data-effect=\"italics\">y<\/em><sup>2<\/sup><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1249480\" data-type=\"problem\">\n<p id=\"fs-id1171103712513\">Identify the like terms in the list or the expression:<\/p>\n<p id=\"fs-id1863655\">\\(4{x}^{3}+8{x}^{2}+19+3{x}^{2}+24+6{x}^{3}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2650561\" data-type=\"solution\"><details><summary>Show Answer<\/summary>4<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 6<em data-effect=\"italics\">x<\/em><sup>3<\/sup>; 8<em data-effect=\"italics\">x<\/em><sup>2<\/sup> and 3<em data-effect=\"italics\">x<\/em><sup>2<\/sup>; 19 and 24\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Combining Like Terms<\/h1>\n<p id=\"fs-id1169528\">We can simplify an expression by combining the <span class=\"no-emphasis\" data-type=\"term\">like terms<\/span>. What do you think \\(3x+6x\\) would simplify to? If you thought \\(9x\\), you would be right!<\/p>\n<p id=\"fs-id1374385\">We can see why this works by writing both terms as addition problems.<\/p>\n<span id=\"fs-id2261867\" data-type=\"media\" data-alt=\"The image shows the expression 3 x plus 6 x. The 3 x represents x plus x plus x. The 6 x represents x plus x plus x plus x plus x plus x. The expression 3 x plus 6 x becomes x plus x plus x plus x plus x plus x plus x plus x plus x. This simplifies to a total of 9 x's or the term 9 x.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_001_img-1.jpg\" alt=\"The image shows the expression 3 x plus 6 x. The 3 x represents x plus x plus x. The 6 x represents x plus x plus x plus x plus x plus x. The expression 3 x plus 6 x becomes x plus x plus x plus x plus x plus x plus x plus x plus x. This simplifies to a total of 9 x's or the term 9 x.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1693610\">Add the <span class=\"no-emphasis\" data-type=\"term\">coefficients<\/span> and keep the same variable. It doesn\u2019t matter what \\(x\\) is. If you have \\(3\\) of something and add \\(6\\) more of the same thing, the result is \\(9\\) of them. For example, \\(3\\) oranges plus \\(6\\) oranges is \\(9\\) oranges. We will discuss the mathematical properties behind this later.<\/p>\nThe expression \\(3x+6x\\) has only two terms. When an expression contains more terms, it may be helpful to rearrange the terms so that like terms are together. The <span class=\"no-emphasis\" data-type=\"term\">Commutative Property of Addition<\/span> says that we can change the order of addends without changing the sum. So we could rearrange the following expression before combining like terms.\n\n<span id=\"fs-id1605094\" data-type=\"media\" data-alt=\"The image shows the expression 3 x plus 4 y plus 2 x plus 6 y. The position of the middle terms, 4 y and 2 x, can be switched so that the expression becomes 3 x plus 2 x plus 4 y plus 6 y. Now the terms containing x are together and the terms containing y are together.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_015_img-1.jpg\" alt=\"The image shows the expression 3 x plus 4 y plus 2 x plus 6 y. The position of the middle terms, 4 y and 2 x, can be switched so that the expression becomes 3 x plus 2 x plus 4 y plus 6 y. Now the terms containing x are together and the terms containing y are together.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1364178\">Now it is easier to see the like terms to be combined.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Combine like terms<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168466010921\" class=\"stepwise\" type=\"1\">\n \t<li>Identify like terms.<\/li>\n \t<li>Rearrange the expression so like terms are together.<\/li>\n \t<li>Add the coefficients of the like terms.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1883861\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2436213\" data-type=\"problem\">\n\nSimplify the expression: \\(3x+7+4x+5\\).\n\n<\/div>\n<div id=\"fs-id1547208\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168468738000\" class=\"unnumbered unstyled\" summary=\"The image shows the expression 3 x plus 7 plus 4 x plus 5. Three x and 4 x are like terms as are 7 and 5. The middle terms, 7 and 4 x, can be rearranged so that the like terms are together. The expressions becomes 3 x plus 4 x plus 7 plus 5. Now the like terms can be combined by adding the coefficients of the like terms. Three x plus 4 x is 7 x and 7 plus 5 is 12. The expression becomes 7 x plus 12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468738019\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the like terms.<\/td>\n<td><span id=\"eip-id1168468738036\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the expression, so the like terms are together.<\/td>\n<td><span id=\"eip-id1168468738052\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add the coefficients of the like terms.<\/td>\n<td><span id=\"eip-id1168468373750\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The original expression is simplified to...<\/td>\n<td><span id=\"eip-id1168468373766\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1788985\">Simplify:<\/p>\n<p id=\"fs-id1231921\">\\(7x+9+9x+8\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2881634\" data-type=\"solution\"><details><summary>Show Answer<\/summary>16<em data-effect=\"italics\">x<\/em> + 17\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1967025\" data-type=\"problem\">\n<p id=\"fs-id1171105545984\">Simplify:<\/p>\n\\(5y+2+8y+4y+5\\)\n\n<\/div>\n<div id=\"fs-id2860845\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1205903\">17<em data-effect=\"italics\">y<\/em> + 7<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id793755\">Simplify the expression: \\(7{x}^{2}+8x+{x}^{2}+4x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2203129\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168467195542\" class=\"unnumbered unstyled\" summary=\"The image shows the expression 7 x squared plus 8 x plus x squared plus 4 x. Seven x squared and x squared are like terms as are 8 x and 4 x. The middle terms, 8 x and x squared, can be rearranged so that the like terms are together. The expressions becomes 7 x squared plus x squared plus 8 x plus 4 x. Now the like terms can be combined by adding the coefficients of the like terms. 7 x squared plus x squared is 8 x squared and 8 x plus 4 x is 12 x. The expression becomes 8 x squared plus 12 x.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467195560\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the like terms.<\/td>\n<td><span id=\"eip-id1168467195577\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the expression so like terms are together.<\/td>\n<td><span id=\"eip-id1168467195594\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add the coefficients of the like terms.<\/td>\n<td><span id=\"eip-id1168468740579\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nThese are not like terms and cannot be combined. So \\(8{x}^{2}+12x\\) is in simplest form.\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103505074\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1369298\" data-type=\"exercise\">\n<div id=\"fs-id2860845\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id295588\" data-type=\"problem\">\n<p id=\"fs-id2702656\">Simplify:<\/p>\n<p id=\"fs-id1605168\">\\(3{x}^{2}+9x+{x}^{2}+5x\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1548701\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1858346\">4<em data-effect=\"italics\">x<\/em><sup>2<\/sup> + 14<em data-effect=\"italics\">x<\/em><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1341641\" data-type=\"problem\">\n<p id=\"fs-id1171105113756\">Simplify:<\/p>\n<p id=\"fs-id2375181\">\\(11{y}^{2}+8y+{y}^{2}+7y\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1184392\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id4445444\">12<em data-effect=\"italics\">y<\/em><sup>2<\/sup> + 15<em data-effect=\"italics\">y<\/em><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate Words to Algebraic Expressions<\/h1>\n<p id=\"fs-id1951299\">In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we\u2019ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we\u2019ve talked about will help us do that. They are summarized in the table below.<\/p>\n\n<table id=\"eip-386\" class=\"grid\" style=\"width: 100%;\" summary=\".\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left; width: 25%;\" scope=\"col\" data-align=\"center\">Operation<\/th>\n<th style=\"text-align: left; width: 50%;\" scope=\"col\" data-align=\"center\">Phrase<\/th>\n<th style=\"text-align: left; width: 25%;\" scope=\"col\" data-align=\"center\">Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Addition<\/td>\n<td data-align=\"left\">\\(a\\) plus \\(b\\)\nthe sum of \\(a\\) and \\(b\\)\n\\(a\\) increased by \\(b\\)\n\\(b\\) more than \\(a\\)\nthe total of \\(a\\) and \\(b\\)\n\\(b\\) added to \\(a\\)<\/td>\n<td data-valign=\"top\" data-align=\"center\">\\(a+b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Subtraction<\/td>\n<td data-align=\"left\">\\(a\\) minus \\(b\\)\nthe difference of \\(a\\) and \\(b\\)\n\\(b\\) subtracted from \\(a\\)\n\\(a\\) decreased by \\(b\\)\n\\(b\\) less than \\(a\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(a-b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Multiplication<\/td>\n<td data-align=\"left\">\\(a\\) times \\(b\\)\nthe product of \\(a\\) and \\(b\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(a\\cdot b\\), \\(ab\\), \\(a\\left(b\\right)\\), \\(\\left(a\\right)\\left(b\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Division<\/td>\n<td data-align=\"left\">\\(a\\) divided by \\(b\\)\nthe quotient of \\(a\\) and \\(b\\)\nthe ratio of \\(a\\) and \\(b\\)\n\\(b\\) divided into \\(a\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(a \\div b\\), \\(a\/b\\), \\(\\frac{a}{b}\\), \\(b\\overline{)a}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2908409\">Look closely at these phrases using the four operations:<\/p>\n\n<ul id=\"fs-id1171105561839\" data-bullet-style=\"bullet\">\n \t<li>the sum <em data-effect=\"italics\">of<\/em> \\(a\\) <em data-effect=\"italics\">and<\/em> \\(b\\)<\/li>\n \t<li>the difference <em data-effect=\"italics\">of<\/em> \\(a\\) <em data-effect=\"italics\">and<\/em> \\(b\\)<\/li>\n \t<li>the product <em data-effect=\"italics\">of<\/em> \\(a\\) <em data-effect=\"italics\">and<\/em> \\(b\\)<\/li>\n \t<li>the quotient <em data-effect=\"italics\">of<\/em> \\(a\\) <em data-effect=\"italics\">and<\/em> \\(b\\)<\/li>\n<\/ul>\n<p id=\"fs-id2267592\">Each phrase tells you to operate on two numbers. Look for the words <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> and <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> to find the numbers.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1736728\" data-type=\"problem\">\n<p id=\"fs-id2214080\">Translate each word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168467166071\" class=\"circled\" type=\"a\">\n \t<li>\u00a0the difference of \\(20\\) and \\(4\\)<\/li>\n \t<li>\u00a0the quotient of \\(10x\\) and \\(3\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1761830\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2399214\">a. The key word is <em data-effect=\"italics\">difference<\/em>, which tells us the operation is subtraction. Look for the words <em data-effect=\"italics\">of<\/em> and <em data-effect=\"italics\">and<\/em> to find the numbers to subtract.<\/p>\n<p id=\"fs-id2208916\">\\(\\begin{array}{cccc}\\\\ \\text{the difference}\\phantom{\\rule{0.2em}{0ex}}\\text{of}\\phantom{\\rule{0.2em}{0ex}}20\\phantom{\\rule{0.2em}{0ex}}and\\phantom{\\rule{0.2em}{0ex}}4\\hfill \\\\ 20\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}4\\hfill \\\\ 20-4\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id1269652\">b. The key word is <em data-effect=\"italics\">quotient<\/em>, which tells us the operation is division.<\/p>\n<p id=\"fs-id14671710\">\\(\\begin{array}{ccccc}\\\\ \\text{the quotient of}\\phantom{\\rule{0.2em}{0ex}}10x\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}3\\hfill \\\\ \\text{divide}\\phantom{\\rule{0.2em}{0ex}}10x\\phantom{\\rule{0.2em}{0ex}}\\text{by}\\phantom{\\rule{0.2em}{0ex}}3\\hfill \\\\ 10x\\div 3\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id1171105493688\">This can also be written as \\(\\begin{array}{l}10x\/3\\phantom{\\rule{0.2em}{0ex}}\\text{or}\\phantom{\\rule{0.4em}{0ex}}\\frac{10x}{3}\\hfill \\end{array}\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1973372\" data-type=\"problem\">\n<p id=\"fs-id2212147\">Translate the given word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168466926674\" class=\"circled\" type=\"a\">\n \t<li>\u00a0the difference of \\(47\\) and \\(41\\)<\/li>\n \t<li>\u00a0the quotient of \\(5x\\) and \\(2\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1379011\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466200991\" class=\"circled\" type=\"a\">\n \t<li>\u00a047 \u2212 41<\/li>\n \t<li>\u00a05<em data-effect=\"italics\">x<\/em> \u00f7 2<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1614102\" data-type=\"problem\">\n<p id=\"fs-id1171105421723\">Translate the given word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168465992356\" class=\"circled\" type=\"a\">\n \t<li>\u00a0the sum of \\(17\\) and \\(19\\)<\/li>\n \t<li>\u00a0the product of \\(7\\) and \\(x\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2150850\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466080789\" class=\"circled\" type=\"a\">\n \t<li>\u00a017 + 19<\/li>\n \t<li>\u00a07<em data-effect=\"italics\">x<\/em><\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1627292\">How old will you be in eight years? What age is eight more years than your age now? Did you add \\(8\\) to your present age? Eight <em data-effect=\"italics\">more than<\/em> means eight added to your present age.<\/p>\n<p id=\"fs-id2495303\">How old were you seven years ago? This is seven years less than your age now. You subtract \\(7\\) from your present age. Seven <em data-effect=\"italics\">less than<\/em> means seven subtracted from your present age.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2204468\" data-type=\"problem\">\n<p id=\"fs-id2700294\">Translate each word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168467351341\" class=\"circled\" type=\"a\">\n \t<li>\u00a0Eight more than \\(y\\)<\/li>\n \t<li>\u00a0Seven less than \\(9z\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1205457\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1374015\">a. The key words are <em data-effect=\"italics\">more than<\/em>. They tell us the operation is addition. <em data-effect=\"italics\">More than<\/em> means \u201cadded to\u201d.<\/p>\n<p id=\"fs-id2284969\">\\(\\begin{array}{l}\\text{Eight more than}\\phantom{\\rule{0.2em}{0ex}}y\\\\ \\text{Eight added to}\\phantom{\\rule{0.2em}{0ex}}y\\\\ y+8\\end{array}\\)<\/p>\n<p id=\"fs-id2785746\">b. The key words are <em data-effect=\"italics\">less than<\/em>. They tell us the operation is subtraction. <em data-effect=\"italics\">Less than<\/em> means \u201csubtracted from\u201d.<\/p>\n<p id=\"fs-id2190936\">\\(\\begin{array}{l}\\text{Seven less than}\\phantom{\\rule{0.2em}{0ex}}9z\\\\ \\text{Seven subtracted from}\\phantom{\\rule{0.2em}{0ex}}9z\\\\ 9z-7\\end{array}\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2203045\" data-type=\"problem\">\n<p id=\"fs-id2266808\">Translate each word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168468303099\" class=\"circled\" type=\"a\">\n \t<li>\u00a0Eleven more than \\(x\\)<\/li>\n \t<li>\u00a0Fourteen less than \\(11a\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1748485\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469857801\" class=\"circled\" type=\"a\">\n \t<li><em data-effect=\"italics\">x<\/em> + 11<\/li>\n \t<li>11<em data-effect=\"italics\">a<\/em> \u2212 14<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1278868\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1269389\" data-type=\"exercise\">\n<div id=\"fs-id2203045\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1458006\" data-type=\"problem\">\n<p id=\"fs-id1171105138387\">Translate each word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168468371000\" class=\"circled\" type=\"a\">\n \t<li>\\(19\\) more than \\(j\\)<\/li>\n \t<li>\\(21\\) less than \\(2x\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1881448\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467258633\" class=\"circled\" type=\"a\">\n \t<li><em data-effect=\"italics\">j<\/em> + 19<\/li>\n \t<li>2<em data-effect=\"italics\">x<\/em> \u2212 21<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105461719\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2257971\" data-type=\"exercise\">\n<div id=\"fs-id1458006\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2206433\" data-type=\"problem\">\n<p id=\"fs-id1572229\">Translate each word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168468738249\" class=\"circled\" type=\"a\">\n \t<li>five times the sum of \\(m\\) and \\(n\\)<\/li>\n \t<li>the sum of five times \\(m\\) and \\(n\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2211545\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1630800\">a. There are two operation words: <em data-effect=\"italics\">times<\/em> tells us to multiply and <em data-effect=\"italics\">sum<\/em> tells us to add. Because we are multiplying \\(5\\) times the sum, we need parentheses around the sum of \\(m\\) and \\(n\\).<\/p>\n<p id=\"fs-id2299604\">five times the sum of \\(m\\) and \\(n\\)\n\\(\\begin{array}{cccc}\\\\ \\\\ \\phantom{\\rule{4em}{0ex}}5\\left(m+n\\right)\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id1582880\">b. To take a sum, we look for the words <em data-effect=\"italics\">of<\/em> and <em data-effect=\"italics\">and<\/em> to see what is being added. Here we are taking the sum <em data-effect=\"italics\">of<\/em> five times \\(m\\) and \\(n\\).<\/p>\n<p id=\"fs-id1823388\">the sum of five times \\(m\\) and \\(n\\)\n\\(\\begin{array}{ccccc}\\\\ \\\\ \\phantom{\\rule{4em}{0ex}}5m+n\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id2696230\">Notice how the use of parentheses changes the result. In part a), we add first and in part b), we multiply first.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2785111\" data-type=\"problem\">\n<p id=\"fs-id2642905\">Translate the word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168468228349\" class=\"circled\" type=\"a\">\n \t<li>four times the sum of \\(p\\) and \\(q\\)<\/li>\n \t<li>the sum of four times \\(p\\) and \\(q\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2657948\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469868809\" class=\"circled\" type=\"a\">\n \t<li>4(<em data-effect=\"italics\">p<\/em> + <em data-effect=\"italics\">q<\/em>)<\/li>\n \t<li>4<em data-effect=\"italics\">p<\/em> + <em data-effect=\"italics\">q<\/em><\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1971669\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1362744\" data-type=\"exercise\">\n<div id=\"fs-id2785111\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id3399510\" data-type=\"problem\">\n<p id=\"fs-id1171101791128\">Translate the word phrase into an algebraic expression:<\/p>\n\n<ol id=\"eip-id1168466313766\" class=\"circled\" type=\"a\">\n \t<li>the difference of two times \\(x\\phantom{\\rule{0.2em}{0ex}}\\text{and 8}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>two times the difference of \\(x\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}8\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2270755\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466165177\" class=\"circled\" type=\"a\">\n \t<li>2<em data-effect=\"italics\">x<\/em> \u2212 8<\/li>\n \t<li>2(<em data-effect=\"italics\">x<\/em> \u2212 8)<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\nLater in this course, we\u2019ll apply our skills in algebra to solving equations. We\u2019ll usually start by translating a word phrase to an algebraic expression. We\u2019ll need to be clear about what the expression will represent. We\u2019ll see how to do this in the next two examples.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1932541\" data-type=\"problem\">\n<p id=\"fs-id1481031\">The height of a rectangular window is \\(6\\) inches less than the width. Let \\(w\\) represent the width of the window. Write an expression for the height of the window.<\/p>\n\n<\/div>\n<div id=\"fs-id1258807\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168466033010\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">Write a phrase about the height.<\/td>\n<td style=\"width: 50%;\">\\(6\\) less than the width<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Substitute \\(w\\) for the width.<\/td>\n<td style=\"width: 50%;\">\\(6\\) less than \\(w\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite 'less than' as 'subtracted from'.<\/td>\n<td style=\"width: 50%;\">\\(6\\) subtracted from \\(w\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate the phrase into algebra.<\/td>\n<td style=\"width: 50%;\">\\(w-6\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2700289\" data-type=\"problem\">\n<p id=\"fs-id2274284\">The length of a rectangle is \\(5\\) inches less than the width. Let \\(w\\) represent the width of the rectangle. Write an expression for the length of the rectangle.<\/p>\n\n<\/div>\n<div id=\"fs-id1693128\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1693130\"><em data-effect=\"italics\">w<\/em> \u2212 5<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id2785835\">The width of a rectangle is \\(2\\) metres greater than the length. Let \\(l\\) represent the length of the rectangle. Write an expression for the width of the rectangle.<\/p>\n\n<\/div>\n<div id=\"fs-id1795902\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id4120698\"><em data-effect=\"italics\">l<\/em> + 2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1602816\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2161945\" data-type=\"exercise\">\n<div id=\"fs-id2700289\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1866171\" data-type=\"problem\">\n<p id=\"fs-id2603709\">Blanca has dimes and quarters in her purse. The number of dimes is \\(2\\) less than \\(5\\) times the number of quarters. Let \\(q\\) represent the number of quarters. Write an expression for the number of dimes.<\/p>\n\n<\/div>\n<div id=\"fs-id2451560\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168467234223\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Write a phrase about the number of dimes.<\/td>\n<td>two less than five times the number of quarters<\/td>\n<\/tr>\n<tr>\n<td>Substitute \\(q\\) for the number of quarters.<\/td>\n<td>\\(2\\) less than five times \\(q\\)<\/td>\n<\/tr>\n<tr>\n<td>Translate \\(5\\) <em data-effect=\"italics\">times<\/em> \\(q\\).<\/td>\n<td>\\(2\\) less than \\(5q\\)<\/td>\n<\/tr>\n<tr>\n<td>Translate the phrase into algebra.<\/td>\n<td>\\(5q-2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1737365\">Geoffrey has dimes and quarters in his pocket. The number of dimes is seven less than six times the number of quarters. Let \\(q\\) represent the number of quarters. Write an expression for the number of dimes.<\/p>\n\n<\/div>\n<div id=\"fs-id1984837\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2644785\">6<em data-effect=\"italics\">q<\/em> \u2212 7<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1816680\" data-type=\"problem\">\n<p id=\"fs-id2567774\">Lauren has dimes and nickels in her purse. The number of dimes is eight more than four times the number of nickels. Let \\(n\\) represent the number of nickels. Write an expression for the number of dimes.<\/p>\n\n<\/div>\n<div id=\"fs-id2389740\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2196387\">4<em data-effect=\"italics\">n<\/em> + 8<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1860727\" class=\"media-2\" data-type=\"note\">\n<div data-type=\"title\">ACCESS ADDITIONAL ONLINE RESOURCES<\/div>\n<ul id=\"fs-id2362976\" data-display=\"block\">\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24AlgExpvocab\">Algebraic Expression Vocabulary<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id2626380\" data-bullet-style=\"bullet\">\n \t<li><strong>Combine like terms.<\/strong>\n<ol id=\"eip-id1168265179478\" class=\"stepwise\" type=\"1\">\n \t<li>Identify like terms.<\/li>\n \t<li>Rearrange the expression so like terms are together.<\/li>\n \t<li>Add the coefficients of the like terms<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1503046\">\n \t<dt>term<\/dt>\n \t<dd id=\"fs-id1891510\">A term is a constant or the product of a constant and one or more variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id2662318\">\n \t<dt>coefficient<\/dt>\n \t<dd id=\"fs-id1301322\">The constant that multiplies the variable(s) in a term is called the coefficient.<\/dd>\n<\/dl>\n<dl id=\"fs-id2961409\">\n \t<dt>like terms<\/dt>\n \t<dd id=\"fs-id1294455\">Terms that are either constants or have the same variables with the same exponents are like terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1549920\">\n \t<dt>evaluate<\/dt>\n \t<dd id=\"fs-id1753163\">To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Evaluate Algebraic Expressions<\/h2>\n<p id=\"eip-663\">In the following exercises, evaluate the expression for the given value.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 272px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">1. \\(7x+8\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=2\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">2. \\(9x+7\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">3. \\(5x-4\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">4. \\(8x-6\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=7\\)<\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 50%; height: 31px;\">5. \\({x}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=12\\)<\/td>\n<td style=\"width: 50%; height: 31px;\">6. \\({x}^{3}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=5\\)<\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 50%; height: 31px;\">7. \\({x}^{5}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=2\\)<\/td>\n<td style=\"width: 50%; height: 31px;\">8. \\({x}^{4}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">9. \\({3}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">10. \\({4}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=2\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">11. \\({x}^{2}+3x-7\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=4\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">12. \\({x}^{2}+5x-8\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">13. \\(2x+4y-5\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=7,y=8\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">14. \\(6x+3y-9\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6,y=9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">15. \\({\\left(x-y\\right)}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=10,y=7\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">16. \\({\\left(x+y\\right)}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6,y=9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">17. \\({a}^{2}+{b}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}a=3,b=8\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">18. \\({r}^{2}-{s}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}r=12,s=5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">19. \\(2l+2w\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}l=15,w=12\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">20. \\(2l+2w\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}l=18,w=14\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Identify Terms, Coefficients, and Like Terms<\/h2>\n<p id=\"eip-413\">In the following exercises, list the terms in the given expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">21. \\(15{x}^{2}+6x+2\\)<\/td>\n<td style=\"width: 50%;\">22. \\(11{x}^{2}+8x+5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. \\(10{y}^{3}+y+2\\)<\/td>\n<td style=\"width: 50%;\">24. \\(9{y}^{3}+y+5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1213539\">In the following exercises, identify the coefficient of the given term.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">25. \\(8a\\)<\/td>\n<td style=\"width: 50%;\">26. \\(13m\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. \\(5{r}^{2}\\)<\/td>\n<td style=\"width: 50%;\">28. \\(6{x}^{3}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1515917\">In the following exercises, identify all sets of like terms.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">29. \\({x}^{3},8x,14,8y,5,8{x}^{3}\\)<\/td>\n<td style=\"width: 50%;\">30. \\(6z,3{w}^{2},1,6{z}^{2},4z,{w}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. \\(9a,{a}^{2},16ab,16{b}^{2},4ab,9{b}^{2}\\)<\/td>\n<td style=\"width: 50%;\">32. \\(3,25{r}^{2},10s,10r,4{r}^{2},3s\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions by Combining Like Terms<\/h2>\n<p id=\"eip-441\">In the following exercises, simplify the given expression by combining like terms.<\/p>\n\n<div id=\"fs-id2265620\" data-type=\"exercise\">\n<div id=\"fs-id2265623\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 120px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">33. \\(10x+3x\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">34. \\(15x+4x\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">35. \\(17a+9a\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">36. \\(18z+9z\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">37. \\(4c+2c+c\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">38. \\(6y+4y+y\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">39. \\(9x+3x+8\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">40. \\(8a+5a+9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">41. \\(7u+2+3u+1\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">42. \\(8d+6+2d+5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">43. \\(7p+6+5p+4\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">44. \\(8x+7+4x-5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. \\(10a+7+5a-2+7a-4\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">46. \\(7c+4+6c-3+9c-1\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. \\(3{x}^{2}+12x+11+14{x}^{2}+8x+5\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">48. \\(5{b}^{2}+9b+10+2{b}^{2}+3b-4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2>Translate English Phrases into Algebraic Expressions<\/h2>\n<p id=\"eip-583\">In the following exercises, translate the given word phrase into an algebraic expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 181px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">49. The sum of 8 and 12<\/td>\n<td style=\"width: 50%; height: 16px;\">50. The sum of 9 and 1<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. The difference of 14 and 9<\/td>\n<td style=\"width: 50%; height: 15px;\">52. 8 less than 19<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. The product of 9 and 7<\/td>\n<td style=\"width: 50%; height: 15px;\">54. The product of 8 and 7<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. The quotient of 36 and 9<\/td>\n<td style=\"width: 50%; height: 15px;\">56. The quotient of 42 and 7<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. The difference of \\(x\\) and \\(4\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">58. \\(3\\) less than \\(x\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. The product of \\(6\\) and \\(y\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">60. The product of \\(9\\) and \\(y\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. The sum of \\(8x\\) and \\(3x\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">62. The sum of \\(13x\\) and \\(3x\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">63. The quotient of \\(y\\) and \\(3\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">64. The quotient of \\(y\\) and \\(8\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">65. Eight times the difference of \\(y\\) and nine<\/td>\n<td style=\"width: 50%; height: 15px;\">66. Seven times the difference of \\(y\\) and one<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">67. Five times the sum of \\(x\\) and \\(y\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">68. \u00a0times five less than twice \\(x\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1334823\">In the following exercises, write an algebraic expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">69. Adele bought a skirt and a blouse. The skirt cost \\$15 more than the blouse. Let \\(b\\) represent the cost of the blouse. Write an expression for the cost of the skirt.<\/td>\n<td style=\"width: 50%;\">70. Eric has rock and classical CDs in his car. The number of rock CDs is \\(3\\) more than the number of classical CDs. Let \\(c\\) represent the number of classical CDs. Write an expression for the number of rock CDs.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. The number of girls in a second-grade class is \\(4\\) less than the number of boys. Let \\(b\\) represent the number of boys. Write an expression for the number of girls.<\/td>\n<td style=\"width: 50%;\">72. Marcella has \\(6\\) fewer male cousins than female cousins. Let \\(f\\) represent the number of female cousins. Write an expression for the number of boy cousins.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">73. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let \\(n\\) represent the number of nickels. Write an expression for the number of pennies.<\/td>\n<td style=\"width: 50%;\">74. Jeannette has \\$5 and \\$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let \\(t\\) represent the number of tens. Write an expression for the number of fives.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<p id=\"fs-id1487340\">In the following exercises, use algebraic expressions to solve the problem.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">75.<strong data-effect=\"bold\"> Car insurance<\/strong> Justin\u2019s car insurance has a \\$750 deductible per incident. This means that he pays \\$750 and his insurance company will pay all costs beyond \\$750. If Justin files a claim for \\$2,100, how much will he pay, and how much will his insurance company pay?<\/td>\n<td style=\"width: 50%;\">76. <strong data-effect=\"bold\">Home insurance<\/strong> Pam and Armando\u2019s home insurance has a \\$2,500 deductible per incident. This means that they pay \\$2,500 and their insurance company will pay all costs beyond \\$2,500. If Pam and Armando file a claim for \\$19,400, how much will they pay, and how much will their insurance company pay?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">77. Explain why \u201cthe sum of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>\u201d is the same as \u201cthe sum of <em data-effect=\"italics\">y<\/em> and <em data-effect=\"italics\">x<\/em>,\u201d but \u201cthe difference of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>\u201d is not the same as \u201cthe difference of <em data-effect=\"italics\">y<\/em> and <em data-effect=\"italics\">x<\/em>.\u201d Try substituting two random numbers for \\(x\\) and \\(y\\) to help you explain.<\/td>\n<td style=\"width: 50%;\">78. Explain the difference between \\(\\text{\u201c4}\\) times the sum of \\(x\\) and \\(y\\text{\u201d}\\) and \u201cthe sum of \\(4\\) times \\(x\\) and \\(y\\text{.\u201d}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse; width: 100%; height: 221px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. 22<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. 26<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. 144<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 32<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. 27<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. 21<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. 41<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 73<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. 54<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 15<em data-effect=\"italics\">x<\/em><sup>2<\/sup>, 6<em data-effect=\"italics\">x<\/em>, 2<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. 10<em data-effect=\"italics\">y<\/em><sup>3<\/sup>, <em data-effect=\"italics\">y<\/em>, 2<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. 5<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. <em data-effect=\"italics\">x<\/em><sup>3<\/sup>, 8<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 14, 5<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 16<em data-effect=\"italics\">ab<\/em> and 4<em data-effect=\"italics\">ab<\/em>; 16<em data-effect=\"italics\">b<\/em><sup>2<\/sup> and 9<em data-effect=\"italics\">b<\/em><sup>2<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. 13<em data-effect=\"italics\">x<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. 26<em data-effect=\"italics\">a<\/em><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. 7<em data-effect=\"italics\">c<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. 12<em data-effect=\"italics\">x<\/em> + 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. 10<em data-effect=\"italics\">u<\/em> + 3<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. 12<em data-effect=\"italics\">p<\/em> + 10<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. 22<em data-effect=\"italics\">a<\/em> + 1<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. 17<em data-effect=\"italics\">x<\/em><sup>2<\/sup> + 20<em data-effect=\"italics\">x<\/em> + 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. 8 + 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. 14 \u2212 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. 9 \u22c5 7<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">55. 36 \u00f7 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">57. <em data-effect=\"italics\">x<\/em> \u2212 4<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">59. 6<em data-effect=\"italics\">y<\/em><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">61. 8<em data-effect=\"italics\">x<\/em> + 3<em data-effect=\"italics\">x<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">63. \\(\\frac{y}{3}\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">65. 8 (<em data-effect=\"italics\">y<\/em> \u2212 9)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">67. 5 (<em data-effect=\"italics\">x<\/em> + <em data-effect=\"italics\">y<\/em>)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">69. <em data-effect=\"italics\">b<\/em> + 15<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">71. <em data-effect=\"italics\">b<\/em> \u2212 4<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">73. 2<em data-effect=\"italics\">n<\/em> \u2212 7<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">75. He will pay \\$750. His insurance company will pay \\$1350.<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">77. Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cEvaluate, Simplify, and Translate Expressions\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\n\n<\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Evaluate algebraic expressions<\/li>\n<li>Identify terms, coefficients, and like terms<\/li>\n<li>Simplify expressions by combining like terms<\/li>\n<li>Translate word phrases to algebraic expressions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Evaluate Algebraic Expressions<\/h1>\n<p id=\"fs-id2907739\">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 id=\"fs-id1632121\">To evaluate an algebraic expression means to find the value of the expression when the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> is replaced by a given number. To evaluate an <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>, 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 textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1372248\" data-type=\"problem\">\n<p id=\"fs-id1987806\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/> when<\/p>\n<ol id=\"eip-id1168467157803\" class=\"circled\" type=\"a\">\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cf159f8317f743b90dd6866e5c0abd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fdf95cfa2c8b07b1fdd945963f6d803_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2388055\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1576712\">a. To evaluate, substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> 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><span id=\"eip-id1166566546450\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td><span id=\"eip-id1166566546467\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1166566311657\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_007_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2650628\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id2819088\">b. To evaluate, substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> 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><span id=\"eip-id1166566434247\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMAth_Figure_02_02_008_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td><span id=\"eip-id1166566434264\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_008_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1166566434281\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_008_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1737222\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d28a9fa084bc02bc048b780624acf003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: -1px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1736700\">Notice that we got different results for parts a) and b) even though we started with the same expression. This is because the values used for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> were different. When we evaluate an expression, the value varies depending on the value used for the variable.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2211298\" data-type=\"problem\">\n<p id=\"fs-id1357478\">Evaluate:<\/p>\n<p id=\"fs-id1800084\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63403db3a25d5a4fb94ef6f49568b883_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168467133964\" class=\"circled\" type=\"a\">\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d883677907a4892bdfda94f411f56b41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96169d9dd63d4bc98b517428c243c37f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"50\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1946698\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468303825\" class=\"circled\" type=\"a\">\n<li>\u00a010<\/li>\n<li>\u00a019<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1893299\" data-type=\"problem\">\n<p id=\"fs-id1171105480166\">Evaluate:<\/p>\n<p id=\"fs-id2138650\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b98cfcc22fb2d5e8d8c9d2b9aa5d970e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"84\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol id=\"eip-id1168469871235\" class=\"circled\" type=\"a\">\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a789817cb4af408c5101cf328e243288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f934f931b2eadfe51708b11f446f4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id3293034\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468555320\" class=\"circled\" type=\"a\">\n<li>\u00a04<\/li>\n<li>\u00a012<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2603896\" data-type=\"problem\">\n<p id=\"fs-id1800944\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba13a4de500b8e85ecc2a946289ec74a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#45;&#50;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168468470077\" class=\"circled\" type=\"a\">\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f12ee10180053cf88736a2efc9e4fac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3865a7fcb98e87dd2fd1e2f10e80a7f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1406199\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2311961\">Remember <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7202c73e2795274765d7f01eefc3e3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4dc36d20a7690e84c99b1c91d651a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id3177480\">a. To evaluate the expression when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>, we substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, 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><span id=\"eip-id1168469462986\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469463000\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_02_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168469463011\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469463028\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168469463045\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2440233\">b. To evaluate the expression when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/>, we substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, 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><span id=\"eip-id1168468440960\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468440974\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168468440984\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468441002\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168468441019\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2216151\">Notice that in part a) that we wrote <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cdfa2fe38b12384b657598414c4c1ba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/> and in part b) we wrote <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c641a98a34adadd81cea378969c5d6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\" \/>. Both the dot and the parentheses tell us to multiply.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1368058\" data-type=\"problem\">\n<p id=\"fs-id2451489\">Evaluate:<\/p>\n<p id=\"fs-id2136380\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6eec575b7214298a672afcdad3fe21da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#51;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168469756827\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27e167450fc28128ed466c1b1c929fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3865a7fcb98e87dd2fd1e2f10e80a7f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467257646\" class=\"circled\" type=\"a\">\n<li>\u00a013<\/li>\n<li>\u00a05<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2761352\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1370240\" data-type=\"exercise\">\n<div id=\"fs-id1368058\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2420879\" data-type=\"problem\">\n<p id=\"fs-id1171105140307\">Evaluate:<\/p>\n<p id=\"fs-id1281318\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f84f4e75cd606c071dd1bddcf26defb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#45;&#52;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168466004460\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f680354a8c33e34c9f83da05d1c8f59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d30c35137996ab75504722dafc7ec28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2439809\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468610088\" class=\"circled\" type=\"a\">\n<li>\u00a08<\/li>\n<li>\u00a016<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103512900\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1792161\" data-type=\"exercise\">\n<div id=\"fs-id2420879\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2756986\" data-type=\"problem\">\n<p id=\"fs-id1811335\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2661268\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2214943\">We substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, 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><span id=\"eip-id1168468538220\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468538234\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168468538245\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168468538262\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468538279\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_018_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2197016\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1881940\" data-type=\"problem\">\n<p id=\"fs-id1283634\">Evaluate:<\/p>\n<p id=\"fs-id1498924\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fed379ea7db3c74d46255f30ef2e9a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2296111\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1806491\">64<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1498997\" data-type=\"problem\">\n<p id=\"fs-id1171105158454\">Evaluate:<\/p>\n<p id=\"fs-id1546580\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a8a5345bd438249cfb67f6cb0a24460c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2201260\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1180287\">216<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1863809\" data-type=\"problem\">\n<p id=\"fs-id1325186\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1855f5269f0c29a8b2cceebd55c0394f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"178\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2784321\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1731877\">In 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><span id=\"eip-id1168469574762\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469574776\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168469574787\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168469574804\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469574821\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_019_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1547737\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d138fb64cc6a9225d06fdb1af9ca3a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105339525\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id902234\" data-type=\"exercise\">\n<div id=\"fs-id2201260\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<p id=\"fs-id2630090\">Evaluate:<\/p>\n<p id=\"fs-id2130634\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d06d34886c4542fc6d28d686dce68431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2136192\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1824352\">64<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105139468\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1346408\" data-type=\"exercise\">\n<div id=\"fs-id4363755\" data-type=\"problem\">\n<p id=\"fs-id1171105090102\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Evaluate:<\/p>\n<div id=\"fs-id4363755\" data-type=\"problem\">\n<p id=\"fs-id2657794\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e01c79defb636b84b2a5588f9d291c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2691459\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2326737\">81<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1891867\" data-type=\"problem\">\n<p id=\"fs-id2276108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df75478c368b4adfddab4bce6fcb4516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#43;&#52;&#121;&#45;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"336\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2439822\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2264342\">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><span id=\"eip-id1168467237223\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168467237237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168467237247\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168467237264\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add and subtract left to right.<\/td>\n<td><span id=\"eip-id1168467237280\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_020_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1470900\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82c159a12d32f031e64d98abbc2acb45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#52;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<p id=\"fs-id2267372\">Evaluate:<\/p>\n<p id=\"fs-id1160292\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2c4d72d1b30fe01ea1d5ab6738e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"266\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1630119\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p>33<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1603080\" data-type=\"problem\">\n<p id=\"fs-id1171105115923\">Evaluate:<\/p>\n<p id=\"fs-id1718253\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c5b90377ec6b1c713b7cf0441a406440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#50;&#121;&#45;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"257\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1494384\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2555520\">10<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1369028\" data-type=\"exercise\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1785986\" data-type=\"problem\">\n<p id=\"fs-id2657506\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f149d2f0dfbdbca05e322af1d141715d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"259\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1383958\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2310003\">We need to be careful when an expression has a variable with an exponent. In this expression, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ae30abf586092f073ce5550de99fde9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56b20de91e0dcbf61d8c07b3d538e03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/> and is different from the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b69fdfc9b1be5f69f62258f17748005a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -5px;\" \/>, which means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d464895f10d0ac50f4ac34048556ad4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/>.<\/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><span id=\"eip-id1168466011092\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466011106\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168466011116\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-59cc891325714152bb52ef9a606aa546_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466011141\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168466011158\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1168466011175\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2454530\" data-type=\"problem\">\n<p id=\"fs-id2646106\">Evaluate:<\/p>\n<p id=\"fs-id2265086\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fe49d50b6b73a50e7a7090677e544be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;&#43;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"188\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2835764\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1299685\">40<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1259006\" data-type=\"problem\">\n<p id=\"fs-id1171105115753\">Evaluate:<\/p>\n<p id=\"fs-id1605750\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a32deeea7c54e9f113081c2d9e4f1a8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#45;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"187\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2466793\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p>9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Identify Terms, Coefficients, and Like Terms<\/h1>\n<p id=\"fs-id2487968\">Algebraic expressions are made up of <em data-effect=\"italics\">terms<\/em>. A term is a constant or the product of a constant and one or more variables. Some examples of terms are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31f0c01a8e236fd1423c046f477d560d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#44;&#121;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#57;&#97;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#51;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1965867\">The constant that multiplies the variable(s) in a term is called the coefficient. We can think of the coefficient as the number <em data-effect=\"italics\">in front of<\/em> the variable. The coefficient of the term <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>. When we write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, the coefficient is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>, since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ab7cc8a0965d4d7c5b888a274a367a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/>. The table below gives the coefficients for each of the terms in the left column.<\/p>\n<table id=\"fs-id2266631\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cTerm\u201d and the second \u201cCoefficient\u201d. The next row has the number 7 in the \u201cTerm\u201d column and the number 7 in the \u201cCoefficient\u201d column. The next row has the term 9 a in the \u201cTerm\u201d column and the number 9 in the \u201cCoefficient\u201d column. The next row has the letter y in the \u201cTerm\u201d column and the number 1 in the \u201cCoefficient\u201d column. The last row has the term 5 x squared in the \u201cTerm\u201d column and the number 5 in the \u201cCoefficient\u201d column.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\">Term<\/th>\n<th scope=\"col\" data-align=\"center\">Coefficient<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01cced77abd964e948b631893f1d5fdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baa0c10f3b651189378ee7bb755eaf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id3011311\">An algebraic expression may consist of one or more terms added or subtracted. In this chapter, we will only work with terms that are added together. The table below gives some examples of algebraic expressions with various numbers of terms. Notice that we include the operation before a term with it.<\/p>\n<table id=\"fs-id1596496\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d and the second \u201cTerms\u201d. The next row has the number 7 in the \u201cExpression\u201d column and the number 7 in the \u201cTerms\u201d column. The next row has the letter y in the \u201cExpression\u201d column and the letter y in the \u201cTerms\u201d column. The next row has the expression x plus 7 in the \u201cExpression\u201d column and the letter x and the number 7 listed in the \u201cTerms\u201d column. The next row has the expression 2 x plus 7 y plus 4 in the \u201cExpression\u201d column and the terms 2 x, 7 y, and 4 listed in the \u201cTerms\u201d column. The last row has the expression 3 x squared plus 4 x squared plus 5 y plus 3 in the \u201cExpression\u201d column and the terms 3 x squared, 4 x squared, 5 y and 3 listed in the \u201cTerms\u201d column.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\">Expression<\/th>\n<th scope=\"col\" data-align=\"center\">Terms<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3b43381344628d37ffb3820ddf1d540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#44;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"27\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00761db2a6efb3e2f790a3c496084d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#55;&#121;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf29bc9abcaf56837406a7a2b068e4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#44;&#55;&#121;&#44;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41ed3a3a52eb2cdb1c13ca952f07df85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#121;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc7bd55eec9c51e13bb760be7ae2492d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#53;&#121;&#44;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1919072\" data-type=\"problem\">\n<p id=\"fs-id1512228\">Identify each term in the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5400fcfe7ac5b174816dc85a98c59029_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#98;&#43;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#97;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"135\" style=\"vertical-align: -2px;\" \/>. Then identify the coefficient of each term.<\/p>\n<\/div>\n<div id=\"fs-id1823248\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2581602\">The expression has four terms. They are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d4f3f47099013d48d407d6288d06fba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#98;&#44;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1405969\">The coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94451680ba4430cb7a0bf7edeb148c64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id2593979\">The coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c7ed30434ead131ed1441413d8f09f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1944608\">Remember that if no number is written before a variable, the coefficient is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>. So the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id2265026\">The coefficient of a constant is the constant, so the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2281474\" data-type=\"problem\">\n<p id=\"fs-id1620052\">Identify all terms in the given expression, and their coefficients:<\/p>\n<p id=\"fs-id2307665\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-989c14a87fb3536de2ce5eccc4ff149a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#98;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1534340\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2786022\">The terms are 4<em data-effect=\"italics\">x<\/em>, 3<em data-effect=\"italics\">b<\/em>, and 2. The coefficients are 4, 3, and 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1171103838018\">Identify all terms in the given expression, and their coefficients:<\/p>\n<p id=\"fs-id1335442\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a9a4ec9efe60cb2a05637198d9773a10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#97;&#43;&#49;&#51;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#97;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"112\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1575179\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id883422\">The terms are 9<em data-effect=\"italics\">a<\/em>, 13<em data-effect=\"italics\">a<\/em><sup>2<\/sup>, and <em data-effect=\"italics\">a<\/em><sup>3<\/sup>, The coefficients are 9, 13, and 1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Some terms share common traits. Look at the following terms. Which ones seem to have traits in common?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e7dcfd3c83cd3a909952b895eba3f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#44;&#55;&#44;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#44;&#51;&#120;&#44;&#57;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<p id=\"fs-id1283119\">Which of these terms are like terms?<\/p>\n<ul id=\"fs-id1627987\" data-bullet-style=\"bullet\">\n<li>The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> are both constant terms.<\/li>\n<li>The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6093d29b7c98d4d53162882fe6703e10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> are both terms with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-444500c4e43e38956dd248f19f2f7129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25f8f5b2e125247b58f799d23dc7005f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/> both have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-444500c4e43e38956dd248f19f2f7129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1372814\">Terms are called like terms if they have the same variables and exponents. All constant terms are also like terms. So among the terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e7dcfd3c83cd3a909952b895eba3f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#44;&#55;&#44;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#44;&#51;&#120;&#44;&#57;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -4px;\" \/>,<\/p>\n<div id=\"fs-id2268628\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d34a7995d77b10be4bdfd02ef4f755c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"167\" style=\"vertical-align: -1px;\" \/><\/div>\n<div id=\"fs-id555738\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-648981bcceb28fb5eecc2b56c8d334c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"187\" style=\"vertical-align: -1px;\" \/><\/div>\n<div id=\"fs-id2662299\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c5862adf4edabe4ac992e02c498ae1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"195\" style=\"vertical-align: -1px;\" \/><\/div>\n<div id=\"fs-id2129414\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Like Terms<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Terms that are either constants or have the same variables with the same exponents are like terms.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Identify the like terms:<\/p>\n<ol id=\"eip-id1168468588896\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f22415bdc16c81a6b17b2d00ba75a1b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#52;&#44;&#50;&#51;&#44;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#120;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecf26d1fcfec980ea64fb59aab518c39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#43;&#52;&#48;&#120;&#43;&#56;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"255\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2142618\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1190825\">a. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f22415bdc16c81a6b17b2d00ba75a1b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#52;&#44;&#50;&#51;&#44;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#120;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1335628\">Look at the variables and exponents. The expression contains <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f9ca96a7e48d003a26090624975ba5f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"61\" style=\"vertical-align: -4px;\" \/>, and constants.<\/p>\n<p id=\"fs-id1587743\">The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1636a6f930103611f98b9c915049d17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ea159606f98e25800156f98ec07e2eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/> are like terms because they both have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1636a6f930103611f98b9c915049d17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1408738\">The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56fc7ebd82b7bb8226aae7f1108c5256_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baa0c10f3b651189378ee7bb755eaf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> are like terms because they both have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1531249\">The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> are like terms because they are both constants.<\/p>\n<p>The term <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4dc36d20a7690e84c99b1c91d651a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> does not have any like terms in this list since no other terms have the variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> raised to the power of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id2649666\">b. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecf26d1fcfec980ea64fb59aab518c39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#43;&#52;&#48;&#120;&#43;&#56;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"255\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id2495896\">Look at the variables and exponents. The expression contains the terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-239ba622f681be377810882c8b4a4838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#50;&#120;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#54;&#120;&#44;&#52;&#48;&#120;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1462544\">The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06f7fb33ee72b9f6b38da946a36b77cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baa0c10f3b651189378ee7bb755eaf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> are like terms because they both have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1194075\">The terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5dbace405b78b690c944a6537c01a48b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#44;&#54;&#120;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"114\" style=\"vertical-align: -4px;\" \/> are like terms because they all have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id2173435\">The term <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32c0d1ae1f38e3809c705f70ee1349dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\" \/> has no like terms in the given expression because no other terms contain the two variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6f7207ba38a07b82dab0ec08e298c6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1581991\">Identify the like terms in the list or the expression:<\/p>\n<p id=\"fs-id1335600\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eaec3ad2ed4d5fe3fd5d4c99632622d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#44;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#53;&#44;&#57;&#121;&#44;&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1886900\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2481939\">9, 15; 2<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 8<em data-effect=\"italics\">x<\/em><sup>3<\/sup>, <em data-effect=\"italics\">y<\/em><sup>2<\/sup>, and 11<em data-effect=\"italics\">y<\/em><sup>2<\/sup><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1249480\" data-type=\"problem\">\n<p id=\"fs-id1171103712513\">Identify the like terms in the list or the expression:<\/p>\n<p id=\"fs-id1863655\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b99d49c84af9fb6f94d3223ab3c6cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#57;&#43;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#52;&#43;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"250\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2650561\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p>4<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 6<em data-effect=\"italics\">x<\/em><sup>3<\/sup>; 8<em data-effect=\"italics\">x<\/em><sup>2<\/sup> and 3<em data-effect=\"italics\">x<\/em><sup>2<\/sup>; 19 and 24<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions by Combining Like Terms<\/h1>\n<p id=\"fs-id1169528\">We can simplify an expression by combining the <span class=\"no-emphasis\" data-type=\"term\">like terms<\/span>. What do you think <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-255065d909d71427314e6d16b9a88faa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/> would simplify to? If you thought <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4dc36d20a7690e84c99b1c91d651a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>, you would be right!<\/p>\n<p id=\"fs-id1374385\">We can see why this works by writing both terms as addition problems.<\/p>\n<p><span id=\"fs-id2261867\" data-type=\"media\" data-alt=\"The image shows the expression 3 x plus 6 x. The 3 x represents x plus x plus x. The 6 x represents x plus x plus x plus x plus x plus x. The expression 3 x plus 6 x becomes x plus x plus x plus x plus x plus x plus x plus x plus x. This simplifies to a total of 9 x's or the term 9 x.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_001_img-1.jpg\" alt=\"The image shows the expression 3 x plus 6 x. The 3 x represents x plus x plus x. The 6 x represents x plus x plus x plus x plus x plus x. The expression 3 x plus 6 x becomes x plus x plus x plus x plus x plus x plus x plus x plus x. This simplifies to a total of 9 x's or the term 9 x.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1693610\">Add the <span class=\"no-emphasis\" data-type=\"term\">coefficients<\/span> and keep the same variable. It doesn\u2019t matter what <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is. If you have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> of something and add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> more of the same thing, the result is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> of them. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> oranges plus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> oranges is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> oranges. We will discuss the mathematical properties behind this later.<\/p>\n<p>The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-255065d909d71427314e6d16b9a88faa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/> has only two terms. When an expression contains more terms, it may be helpful to rearrange the terms so that like terms are together. The <span class=\"no-emphasis\" data-type=\"term\">Commutative Property of Addition<\/span> says that we can change the order of addends without changing the sum. So we could rearrange the following expression before combining like terms.<\/p>\n<p><span id=\"fs-id1605094\" data-type=\"media\" data-alt=\"The image shows the expression 3 x plus 4 y plus 2 x plus 6 y. The position of the middle terms, 4 y and 2 x, can be switched so that the expression becomes 3 x plus 2 x plus 4 y plus 6 y. Now the terms containing x are together and the terms containing y are together.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_015_img-1.jpg\" alt=\"The image shows the expression 3 x plus 4 y plus 2 x plus 6 y. The position of the middle terms, 4 y and 2 x, can be switched so that the expression becomes 3 x plus 2 x plus 4 y plus 6 y. Now the terms containing x are together and the terms containing y are together.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1364178\">Now it is easier to see the like terms to be combined.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Combine like terms<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168466010921\" class=\"stepwise\" type=\"1\">\n<li>Identify like terms.<\/li>\n<li>Rearrange the expression so like terms are together.<\/li>\n<li>Add the coefficients of the like terms.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1883861\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2436213\" data-type=\"problem\">\n<p>Simplify the expression: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1b22258b8ae6192db81e8603b3a315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#55;&#43;&#52;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"120\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1547208\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168468738000\" class=\"unnumbered unstyled\" summary=\"The image shows the expression 3 x plus 7 plus 4 x plus 5. Three x and 4 x are like terms as are 7 and 5. The middle terms, 7 and 4 x, can be rearranged so that the like terms are together. The expressions becomes 3 x plus 4 x plus 7 plus 5. Now the like terms can be combined by adding the coefficients of the like terms. Three x plus 4 x is 7 x and 7 plus 5 is 12. The expression becomes 7 x plus 12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468738019\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the like terms.<\/td>\n<td><span id=\"eip-id1168468738036\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the expression, so the like terms are together.<\/td>\n<td><span id=\"eip-id1168468738052\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add the coefficients of the like terms.<\/td>\n<td><span id=\"eip-id1168468373750\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The original expression is simplified to&#8230;<\/td>\n<td><span id=\"eip-id1168468373766\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_022_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1788985\">Simplify:<\/p>\n<p id=\"fs-id1231921\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ace488141efb92ea1413e6e3be3e769_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#57;&#43;&#57;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"121\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2881634\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p>16<em data-effect=\"italics\">x<\/em> + 17<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1967025\" data-type=\"problem\">\n<p id=\"fs-id1171105545984\">Simplify:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-864a7937ef6c39c710518098495179f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#43;&#50;&#43;&#56;&#121;&#43;&#52;&#121;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2860845\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1205903\">17<em data-effect=\"italics\">y<\/em> + 7<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id793755\">Simplify the expression: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2482ae09c8e5810cef291db57d7ca723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"148\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2203129\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168467195542\" class=\"unnumbered unstyled\" summary=\"The image shows the expression 7 x squared plus 8 x plus x squared plus 4 x. Seven x squared and x squared are like terms as are 8 x and 4 x. The middle terms, 8 x and x squared, can be rearranged so that the like terms are together. The expressions becomes 7 x squared plus x squared plus 8 x plus 4 x. Now the like terms can be combined by adding the coefficients of the like terms. 7 x squared plus x squared is 8 x squared and 8 x plus 4 x is 12 x. The expression becomes 8 x squared plus 12 x.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467195560\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Identify the like terms.<\/td>\n<td><span id=\"eip-id1168467195577\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the expression so like terms are together.<\/td>\n<td><span id=\"eip-id1168467195594\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add the coefficients of the like terms.<\/td>\n<td><span id=\"eip-id1168468740579\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_02_023_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>These are not like terms and cannot be combined. So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c42da486259bd8dec0d2cef0a78156ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"76\" style=\"vertical-align: -2px;\" \/> is in simplest form.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103505074\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1369298\" data-type=\"exercise\">\n<div id=\"fs-id2860845\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id295588\" data-type=\"problem\">\n<p id=\"fs-id2702656\">Simplify:<\/p>\n<p id=\"fs-id1605168\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26b6b5b6617be3ab8d4f71baa710dafa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"148\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1548701\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1858346\">4<em data-effect=\"italics\">x<\/em><sup>2<\/sup> + 14<em data-effect=\"italics\">x<\/em><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1341641\" data-type=\"problem\">\n<p id=\"fs-id1171105113756\">Simplify:<\/p>\n<p id=\"fs-id2375181\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-990d44ff7c1ed3cb354c5d2805db7abe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#43;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1184392\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id4445444\">12<em data-effect=\"italics\">y<\/em><sup>2<\/sup> + 15<em data-effect=\"italics\">y<\/em><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate Words to Algebraic Expressions<\/h1>\n<p id=\"fs-id1951299\">In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we\u2019ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we\u2019ve talked about will help us do that. They are summarized in the table below.<\/p>\n<table id=\"eip-386\" class=\"grid\" style=\"width: 100%;\" summary=\".\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left; width: 25%;\" scope=\"col\" data-align=\"center\">Operation<\/th>\n<th style=\"text-align: left; width: 50%;\" scope=\"col\" data-align=\"center\">Phrase<\/th>\n<th style=\"text-align: left; width: 25%;\" scope=\"col\" data-align=\"center\">Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Addition<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> plus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\nthe sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> increased by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\nthe total of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> added to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38830949a60ce6786a6fdf6309482002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Subtraction<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> minus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\nthe difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> subtracted from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> decreased by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b644d18119c5701b308f883bd50656d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Multiplication<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\nthe product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d83763995e73895ad8faf8733bc7475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7202c73e2795274765d7f01eefc3e3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fdd143628e341ea88cbb24ffc8cc769a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-11db68dcd69ef007043de0cce2af87c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Division<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\nthe quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\nthe ratio of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> divided into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65401688a6d29528762d26ad54fa20d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#100;&#105;&#118;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72ee3e3e7bb21cf8b1813ac844ed2ddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#47;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"26\" style=\"vertical-align: -5px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8459b97fa73367952be2ca8cf9d1326d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fddbe42aab198073079d39764f0afd11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2908409\">Look closely at these phrases using the four operations:<\/p>\n<ul id=\"fs-id1171105561839\" data-bullet-style=\"bullet\">\n<li>the sum <em data-effect=\"italics\">of<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">and<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>the difference <em data-effect=\"italics\">of<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">and<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>the product <em data-effect=\"italics\">of<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">and<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>the quotient <em data-effect=\"italics\">of<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">and<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<p id=\"fs-id2267592\">Each phrase tells you to operate on two numbers. Look for the words <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> and <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> to find the numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1736728\" data-type=\"problem\">\n<p id=\"fs-id2214080\">Translate each word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168467166071\" class=\"circled\" type=\"a\">\n<li>\u00a0the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>\u00a0the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-405a623e7d2a6832578e529d3677c15a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1761830\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2399214\">a. The key word is <em data-effect=\"italics\">difference<\/em>, which tells us the operation is subtraction. Look for the words <em data-effect=\"italics\">of<\/em> and <em data-effect=\"italics\">and<\/em> to find the numbers to subtract.<\/p>\n<p id=\"fs-id2208916\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-186f23950c47a082c9a53f3e4d194ac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#99;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#110;&#100;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#50;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#50;&#48;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"188\" style=\"vertical-align: -33px;\" \/><\/p>\n<p id=\"fs-id1269652\">b. The key word is <em data-effect=\"italics\">quotient<\/em>, which tells us the operation is division.<\/p>\n<p id=\"fs-id14671710\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4141af3da4919d318a2d5018c27500be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#113;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#118;&#105;&#100;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#49;&#48;&#120;&#92;&#100;&#105;&#118;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"191\" style=\"vertical-align: -34px;\" \/><\/p>\n<p id=\"fs-id1171105493688\">This can also be written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5eca5be5060c97449031e57aa6494b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#49;&#48;&#120;&#47;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#120;&#125;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"95\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1973372\" data-type=\"problem\">\n<p id=\"fs-id2212147\">Translate the given word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168466926674\" class=\"circled\" type=\"a\">\n<li>\u00a0the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f1b412c1849ea0b01e61a0a845ca8df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20bf590fc81a78a705705c8aad69df9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>\u00a0the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6093d29b7c98d4d53162882fe6703e10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1379011\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466200991\" class=\"circled\" type=\"a\">\n<li>\u00a047 \u2212 41<\/li>\n<li>\u00a05<em data-effect=\"italics\">x<\/em> \u00f7 2<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1614102\" data-type=\"problem\">\n<p id=\"fs-id1171105421723\">Translate the given word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168465992356\" class=\"circled\" type=\"a\">\n<li>\u00a0the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>\u00a0the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2150850\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466080789\" class=\"circled\" type=\"a\">\n<li>\u00a017 + 19<\/li>\n<li>\u00a07<em data-effect=\"italics\">x<\/em><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1627292\">How old will you be in eight years? What age is eight more years than your age now? Did you add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> to your present age? Eight <em data-effect=\"italics\">more than<\/em> means eight added to your present age.<\/p>\n<p id=\"fs-id2495303\">How old were you seven years ago? This is seven years less than your age now. You subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> from your present age. Seven <em data-effect=\"italics\">less than<\/em> means seven subtracted from your present age.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2204468\" data-type=\"problem\">\n<p id=\"fs-id2700294\">Translate each word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168467351341\" class=\"circled\" type=\"a\">\n<li>\u00a0Eight more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>\u00a0Seven less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f288db7398715f9e07462de5a8e0fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1205457\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1374015\">a. The key words are <em data-effect=\"italics\">more than<\/em>. They tell us the operation is addition. <em data-effect=\"italics\">More than<\/em> means \u201cadded to\u201d.<\/p>\n<p id=\"fs-id2284969\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aee0177419919a32e97ae03950bc8ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#105;&#103;&#104;&#116;&#32;&#109;&#111;&#114;&#101;&#32;&#116;&#104;&#97;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#105;&#103;&#104;&#116;&#32;&#97;&#100;&#100;&#101;&#100;&#32;&#116;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#92;&#92;&#32;&#121;&#43;&#56;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"140\" style=\"vertical-align: -26px;\" \/><\/p>\n<p id=\"fs-id2785746\">b. The key words are <em data-effect=\"italics\">less than<\/em>. They tell us the operation is subtraction. <em data-effect=\"italics\">Less than<\/em> means \u201csubtracted from\u201d.<\/p>\n<p id=\"fs-id2190936\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-597b6b28aad4c65dc589e9951b42a7ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#101;&#118;&#101;&#110;&#32;&#108;&#101;&#115;&#115;&#32;&#116;&#104;&#97;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#122;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#101;&#118;&#101;&#110;&#32;&#115;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#101;&#100;&#32;&#102;&#114;&#111;&#109;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#122;&#92;&#92;&#32;&#57;&#122;&#45;&#55;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"196\" style=\"vertical-align: -22px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2203045\" data-type=\"problem\">\n<p id=\"fs-id2266808\">Translate each word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168468303099\" class=\"circled\" type=\"a\">\n<li>\u00a0Eleven more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\u00a0Fourteen less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b7f6b23d295ebd639cbe12d10fc256d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1748485\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469857801\" class=\"circled\" type=\"a\">\n<li><em data-effect=\"italics\">x<\/em> + 11<\/li>\n<li>11<em data-effect=\"italics\">a<\/em> \u2212 14<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1278868\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1269389\" data-type=\"exercise\">\n<div id=\"fs-id2203045\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1458006\" data-type=\"problem\">\n<p id=\"fs-id1171105138387\">Translate each word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168468371000\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43c82d5bb00a7568d935a12e3bd969dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#106;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da4556c0a02b580047678d308649edf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1881448\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467258633\" class=\"circled\" type=\"a\">\n<li><em data-effect=\"italics\">j<\/em> + 19<\/li>\n<li>2<em data-effect=\"italics\">x<\/em> \u2212 21<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105461719\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2257971\" data-type=\"exercise\">\n<div id=\"fs-id1458006\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2206433\" data-type=\"problem\">\n<p id=\"fs-id1572229\">Translate each word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168468738249\" class=\"circled\" type=\"a\">\n<li>five times the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>the sum of five times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2211545\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1630800\">a. There are two operation words: <em data-effect=\"italics\">times<\/em> tells us to multiply and <em data-effect=\"italics\">sum<\/em> tells us to add. Because we are multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> times the sum, we need parentheses around the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id2299604\">five times the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f85b4f246180309b4fc58db8304c1bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1582880\">b. To take a sum, we look for the words <em data-effect=\"italics\">of<\/em> and <em data-effect=\"italics\">and<\/em> to see what is being added. Here we are taking the sum <em data-effect=\"italics\">of<\/em> five times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1823388\">the sum of five times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12af1c420a7bb4f317d7aac04c21d79f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#109;&#43;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -24px;\" \/><\/p>\n<p id=\"fs-id2696230\">Notice how the use of parentheses changes the result. In part a), we add first and in part b), we multiply first.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2785111\" data-type=\"problem\">\n<p id=\"fs-id2642905\">Translate the word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168468228349\" class=\"circled\" type=\"a\">\n<li>four times the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>the sum of four times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2657948\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469868809\" class=\"circled\" type=\"a\">\n<li>4(<em data-effect=\"italics\">p<\/em> + <em data-effect=\"italics\">q<\/em>)<\/li>\n<li>4<em data-effect=\"italics\">p<\/em> + <em data-effect=\"italics\">q<\/em><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1971669\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1362744\" data-type=\"exercise\">\n<div id=\"fs-id2785111\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id3399510\" data-type=\"problem\">\n<p id=\"fs-id1171101791128\">Translate the word phrase into an algebraic expression:<\/p>\n<ol id=\"eip-id1168466313766\" class=\"circled\" type=\"a\">\n<li>the difference of two times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aba3e76f17d47d4bb6bdbf0759a62ceb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#32;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>two times the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b0d082587b74d1eea63541cb066a3b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2270755\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466165177\" class=\"circled\" type=\"a\">\n<li>2<em data-effect=\"italics\">x<\/em> \u2212 8<\/li>\n<li>2(<em data-effect=\"italics\">x<\/em> \u2212 8)<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Later in this course, we\u2019ll apply our skills in algebra to solving equations. We\u2019ll usually start by translating a word phrase to an algebraic expression. We\u2019ll need to be clear about what the expression will represent. We\u2019ll see how to do this in the next two examples.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1932541\" data-type=\"problem\">\n<p id=\"fs-id1481031\">The height of a rectangular window is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches less than the width. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/> represent the width of the window. Write an expression for the height of the window.<\/p>\n<\/div>\n<div id=\"fs-id1258807\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168466033010\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">Write a phrase about the height.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> less than the width<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/> for the width.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite &#8216;less than&#8217; as &#8216;subtracted from&#8217;.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> subtracted from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Translate the phrase into algebra.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96c64ffbf86ec5750d2dd69e89643de4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2700289\" data-type=\"problem\">\n<p id=\"fs-id2274284\">The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches less than the width. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/> represent the width of the rectangle. Write an expression for the length of the rectangle.<\/p>\n<\/div>\n<div id=\"fs-id1693128\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1693130\"><em data-effect=\"italics\">w<\/em> \u2212 5<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id2785835\">The width of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> metres greater than the length. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> represent the length of the rectangle. Write an expression for the width of the rectangle.<\/p>\n<\/div>\n<div id=\"fs-id1795902\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id4120698\"><em data-effect=\"italics\">l<\/em> + 2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1602816\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2161945\" data-type=\"exercise\">\n<div id=\"fs-id2700289\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1866171\" data-type=\"problem\">\n<p id=\"fs-id2603709\">Blanca has dimes and quarters in her purse. The number of dimes is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> times the number of quarters. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/> represent the number of quarters. Write an expression for the number of dimes.<\/p>\n<\/div>\n<div id=\"fs-id2451560\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168467234223\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>Write a phrase about the number of dimes.<\/td>\n<td>two less than five times the number of quarters<\/td>\n<\/tr>\n<tr>\n<td>Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/> for the number of quarters.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than five times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">times<\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66c73b86a94c0f27a9ba1e74276be766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"17\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate the phrase into algebra.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-938d44352cc257a90364df65c51b0aa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#113;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1737365\">Geoffrey has dimes and quarters in his pocket. The number of dimes is seven less than six times the number of quarters. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac7da57d7f507262338bb5168feb3e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/> represent the number of quarters. Write an expression for the number of dimes.<\/p>\n<\/div>\n<div id=\"fs-id1984837\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2644785\">6<em data-effect=\"italics\">q<\/em> \u2212 7<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1816680\" data-type=\"problem\">\n<p id=\"fs-id2567774\">Lauren has dimes and nickels in her purse. The number of dimes is eight more than four times the number of nickels. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> represent the number of nickels. Write an expression for the number of dimes.<\/p>\n<\/div>\n<div id=\"fs-id2389740\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2196387\">4<em data-effect=\"italics\">n<\/em> + 8<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1860727\" class=\"media-2\" data-type=\"note\">\n<div data-type=\"title\">ACCESS ADDITIONAL ONLINE RESOURCES<\/div>\n<ul id=\"fs-id2362976\" data-display=\"block\">\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24AlgExpvocab\">Algebraic Expression Vocabulary<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id2626380\" data-bullet-style=\"bullet\">\n<li><strong>Combine like terms.<\/strong>\n<ol id=\"eip-id1168265179478\" class=\"stepwise\" type=\"1\">\n<li>Identify like terms.<\/li>\n<li>Rearrange the expression so like terms are together.<\/li>\n<li>Add the coefficients of the like terms<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1503046\">\n<dt>term<\/dt>\n<dd id=\"fs-id1891510\">A term is a constant or the product of a constant and one or more variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id2662318\">\n<dt>coefficient<\/dt>\n<dd id=\"fs-id1301322\">The constant that multiplies the variable(s) in a term is called the coefficient.<\/dd>\n<\/dl>\n<dl id=\"fs-id2961409\">\n<dt>like terms<\/dt>\n<dd id=\"fs-id1294455\">Terms that are either constants or have the same variables with the same exponents are like terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1549920\">\n<dt>evaluate<\/dt>\n<dd id=\"fs-id1753163\">To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Evaluate Algebraic Expressions<\/h2>\n<p id=\"eip-663\">In the following exercises, evaluate the expression for the given value.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 272px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e16637eb089fba02244dee7c25a4b3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-daa81f6f8d71e85da1e6f3b6b3002f42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#43;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"140\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7cba914abc63d432a5a2b6d37e123c24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"140\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a4e6797532ee6e1dcfefdd225c4c4213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"140\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 50%; height: 31px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ad3dfdc33f13dd73f9511eaf357b403_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"116\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 31px;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f554458970e38704b2c151b47491be34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"107\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 50%; height: 31px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1efbd0834e7dd7beef9325b1539f8cf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"107\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 31px;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-514737cdce827618435a8b09c16a83af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1ebf48d0f1d652d5b2ee6e799050bb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"108\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b6f59f584abebffef211245d68ab4dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"107\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f78d3e2ddf361fb6ca5b07cfc9793320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"179\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0fe303d6d582ba0ea1203891c3e7fa08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"179\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2e44810b7759d8205ca8d9240e2e3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#52;&#121;&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#55;&#44;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"229\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b8863fdf155a76734ab322f992a3132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#51;&#121;&#45;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;&#44;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"229\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-62575be5f7ce742d4e28435b9a853a41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#48;&#44;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"210\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d6d42e38d7fccf6dd9db09e95ed4a292_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;&#44;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"202\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-62c617a2febf82190b08efd9afdc7a11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#51;&#44;&#98;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0de57736018e35e85296a0c58cc8aaa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#114;&#61;&#49;&#50;&#44;&#115;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-775b98022dabb968ad02e2f38a710f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#108;&#43;&#50;&#119;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#108;&#61;&#49;&#53;&#44;&#119;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"214\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61aab4e530da3ae41aa638a7bade61e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#108;&#43;&#50;&#119;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#108;&#61;&#49;&#56;&#44;&#119;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"215\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Identify Terms, Coefficients, and Like Terms<\/h2>\n<p id=\"eip-413\">In the following exercises, list the terms in the given expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a1ff261b3b0e30f5ed755d302e771709_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-921442f01765714f7519576379d284ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be90aac7a5527206410c6ac66549a2fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#121;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c8ec584e1826ec8097e79df3c53cba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#121;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1213539\">In the following exercises, identify the coefficient of the given term.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d497f5435a7d652f3dea0607a3ffe64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f180dd65dba4c940582d9d14c529000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba3aebfac2c46e143559574677950149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d19918445f4e2b2e0b44e1ec5e65acce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1515917\">In the following exercises, identify all sets of like terms.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3e706dfb1d3584965a7c7d9ffa0eaae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#56;&#120;&#44;&#49;&#52;&#44;&#56;&#121;&#44;&#53;&#44;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"147\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bdacc4401bd28287bf000ff6e62a426_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#122;&#44;&#51;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#44;&#54;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#122;&#44;&#123;&#119;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8040df31da466ac969eed2ccd929b02a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#97;&#44;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#54;&#97;&#98;&#44;&#49;&#54;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#97;&#98;&#44;&#57;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"192\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24d911e77f13fed89fa6dd66106fdf34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#50;&#53;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#48;&#115;&#44;&#49;&#48;&#114;&#44;&#52;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#44;&#51;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"175\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions by Combining Like Terms<\/h2>\n<p id=\"eip-441\">In the following exercises, simplify the given expression by combining like terms.<\/p>\n<div id=\"fs-id2265620\" data-type=\"exercise\">\n<div id=\"fs-id2265623\" data-type=\"problem\">\n<table style=\"border-collapse: collapse; width: 100%; height: 120px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd73647af7d3b4da358d5a0f81daf9e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#120;&#43;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"68\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ba4ddaaa8eea335ee258034fcb49baa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#120;&#43;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20570a7d43a0f040976f71a88577734e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#97;&#43;&#57;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9187e21f85c2f63c58bfe49a123ba6a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#122;&#43;&#57;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2fefda32af9eae2a4be537e67fa11235_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#99;&#43;&#50;&#99;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8538a2cdb82463356c4abfef231b94dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#121;&#43;&#52;&#121;&#43;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c99b3c658f93e35bfe5b5e37f75fd58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#43;&#51;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a5189397686d50bbf3acd873908cbdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#97;&#43;&#53;&#97;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec739e1ebbcb473653275fcacbfbb679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#117;&#43;&#50;&#43;&#51;&#117;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"120\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35235c2a8a0a022948041bb2fb37629b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#100;&#43;&#54;&#43;&#50;&#100;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cefbd4c8c9c4307f06bd872770385407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#43;&#54;&#43;&#53;&#112;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd6e7079e93692fef2d3e30a3bcb3356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#55;&#43;&#52;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"120\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94fd7ff2fed28d6603ecbf0b3baa8c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#97;&#43;&#55;&#43;&#53;&#97;&#45;&#50;&#43;&#55;&#97;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"198\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-681e5760841a1f1ab0b53ca0f18243c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#99;&#43;&#52;&#43;&#54;&#99;&#45;&#51;&#43;&#57;&#99;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"184\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b23833fcbb2421e1a371b318d5c028e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#43;&#49;&#49;&#43;&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"243\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3d1e3a8f2b8ba056d28af43350214d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#98;&#43;&#49;&#48;&#43;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#98;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"216\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h2>Translate English Phrases into Algebraic Expressions<\/h2>\n<p id=\"eip-583\">In the following exercises, translate the given word phrase into an algebraic expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 181px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">49. The sum of 8 and 12<\/td>\n<td style=\"width: 50%; height: 16px;\">50. The sum of 9 and 1<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. The difference of 14 and 9<\/td>\n<td style=\"width: 50%; height: 15px;\">52. 8 less than 19<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. The product of 9 and 7<\/td>\n<td style=\"width: 50%; height: 15px;\">54. The product of 8 and 7<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. The quotient of 36 and 9<\/td>\n<td style=\"width: 50%; height: 15px;\">56. The quotient of 42 and 7<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. The difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">60. The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. The sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2e766fef3082260b54b584383d424b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">62. The sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b871713f7ff692d7d69c698e58f4d51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">63. The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">64. The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">65. Eight times the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and nine<\/td>\n<td style=\"width: 50%; height: 15px;\">66. Seven times the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and one<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">67. Five times the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">68. \u00a0times five less than twice <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1334823\">In the following exercises, write an algebraic expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">69. Adele bought a skirt and a blouse. The skirt cost &#36;15 more than the blouse. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> represent the cost of the blouse. Write an expression for the cost of the skirt.<\/td>\n<td style=\"width: 50%;\">70. Eric has rock and classical CDs in his car. The number of rock CDs is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> more than the number of classical CDs. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> represent the number of classical CDs. Write an expression for the number of rock CDs.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. The number of girls in a second-grade class is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> less than the number of boys. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> represent the number of boys. Write an expression for the number of girls.<\/td>\n<td style=\"width: 50%;\">72. Marcella has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> fewer male cousins than female cousins. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\" \/> represent the number of female cousins. Write an expression for the number of boy cousins.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">73. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> represent the number of nickels. Write an expression for the number of pennies.<\/td>\n<td style=\"width: 50%;\">74. Jeannette has &#36;5 and &#36;10 bills in her wallet. The number of fives is three more than six times the number of tens. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> represent the number of tens. Write an expression for the number of fives.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<p id=\"fs-id1487340\">In the following exercises, use algebraic expressions to solve the problem.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">75.<strong data-effect=\"bold\"> Car insurance<\/strong> Justin\u2019s car insurance has a &#36;750 deductible per incident. This means that he pays &#36;750 and his insurance company will pay all costs beyond &#36;750. If Justin files a claim for &#36;2,100, how much will he pay, and how much will his insurance company pay?<\/td>\n<td style=\"width: 50%;\">76. <strong data-effect=\"bold\">Home insurance<\/strong> Pam and Armando\u2019s home insurance has a &#36;2,500 deductible per incident. This means that they pay &#36;2,500 and their insurance company will pay all costs beyond &#36;2,500. If Pam and Armando file a claim for &#36;19,400, how much will they pay, and how much will their insurance company pay?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">77. Explain why \u201cthe sum of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>\u201d is the same as \u201cthe sum of <em data-effect=\"italics\">y<\/em> and <em data-effect=\"italics\">x<\/em>,\u201d but \u201cthe difference of <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>\u201d is not the same as \u201cthe difference of <em data-effect=\"italics\">y<\/em> and <em data-effect=\"italics\">x<\/em>.\u201d Try substituting two random numbers for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> to help you explain.<\/td>\n<td style=\"width: 50%;\">78. Explain the difference between <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58fecb28868ae5676017bbe4701c880c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> times the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18819d1304e9620e21ad3d6cb5afccb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -4px;\" \/> and \u201cthe sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd33d06571af250cba56a4bb4b9aba62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse; width: 100%; height: 221px;\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. 22<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. 26<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. 144<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 32<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. 27<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. 21<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. 41<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 73<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. 54<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 15<em data-effect=\"italics\">x<\/em><sup>2<\/sup>, 6<em data-effect=\"italics\">x<\/em>, 2<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. 10<em data-effect=\"italics\">y<\/em><sup>3<\/sup>, <em data-effect=\"italics\">y<\/em>, 2<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. 5<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. <em data-effect=\"italics\">x<\/em><sup>3<\/sup>, 8<em data-effect=\"italics\">x<\/em><sup>3<\/sup> and 14, 5<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 16<em data-effect=\"italics\">ab<\/em> and 4<em data-effect=\"italics\">ab<\/em>; 16<em data-effect=\"italics\">b<\/em><sup>2<\/sup> and 9<em data-effect=\"italics\">b<\/em><sup>2<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. 13<em data-effect=\"italics\">x<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. 26<em data-effect=\"italics\">a<\/em><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. 7<em data-effect=\"italics\">c<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. 12<em data-effect=\"italics\">x<\/em> + 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. 10<em data-effect=\"italics\">u<\/em> + 3<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. 12<em data-effect=\"italics\">p<\/em> + 10<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. 22<em data-effect=\"italics\">a<\/em> + 1<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. 17<em data-effect=\"italics\">x<\/em><sup>2<\/sup> + 20<em data-effect=\"italics\">x<\/em> + 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. 8 + 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. 14 \u2212 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. 9 \u22c5 7<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">55. 36 \u00f7 9<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">57. <em data-effect=\"italics\">x<\/em> \u2212 4<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">59. 6<em data-effect=\"italics\">y<\/em><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">61. 8<em data-effect=\"italics\">x<\/em> + 3<em data-effect=\"italics\">x<\/em><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb943993e20038edba07582a6062b097_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"8\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">65. 8 (<em data-effect=\"italics\">y<\/em> \u2212 9)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">67. 5 (<em data-effect=\"italics\">x<\/em> + <em data-effect=\"italics\">y<\/em>)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">69. <em data-effect=\"italics\">b<\/em> + 15<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">71. <em data-effect=\"italics\">b<\/em> \u2212 4<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">73. 2<em data-effect=\"italics\">n<\/em> \u2212 7<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">75. He will pay &#36;750. His insurance company will pay &#36;1350.<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">77. Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cEvaluate, Simplify, and Translate Expressions\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n","protected":false},"author":90,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-151","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/151\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/151\/revisions\/152"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/151\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=151"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=151"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=151"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}