{"id":6191,"date":"2017-05-01T23:51:10","date_gmt":"2017-05-01T23:51:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=6191"},"modified":"2017-09-23T05:37:37","modified_gmt":"2017-09-23T05:37:37","slug":"use-the-language-of-algebra","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/use-the-language-of-algebra\/","title":{"raw":"Using Variables and Algebraic Notation","rendered":"Using Variables and Algebraic Notation"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use variables to represent unknown quantities in algebraic expressions<\/li>\r\n \t<li>Identify the variables and constants in an algebraic expression<\/li>\r\n \t<li>Use words and symbols to represent algebraic operations on variables and constants<\/li>\r\n \t<li>Use inequality symbols to compare two quantities<\/li>\r\n \t<li>Translate between words and inequality notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 data-type=\"title\">Use Variables and Algebraic Symbols<\/h2>\r\nGreg and Alex have the same birthday, but they were born in different years. This year Greg is [latex]20[\/latex] years old and Alex is [latex]23[\/latex], so Alex is [latex]3[\/latex] years older than Greg. When Greg was [latex]12[\/latex], Alex was [latex]15[\/latex]. When Greg is [latex]35[\/latex], Alex will be [latex]38[\/latex]. No matter what Greg\u2019s age is, Alex\u2019s age will always be [latex]3[\/latex] years more, right?\r\n\r\nIn the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are variable and the three is a constant. The ages change, or vary, so age is a variable. The [latex]3[\/latex] years between them always stays the same, so the age difference is the constant.\r\n\r\nIn algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age [latex]g[\/latex]. Then we could use [latex]g+3[\/latex] to represent Alex\u2019s age. See the table below.\r\n<table style=\"width: 40%;\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Greg\u2019s age<\/th>\r\n<th data-align=\"center\">Alex\u2019s age<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]12[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]20[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]23[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]35[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]38[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]g[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]g+3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLetters are used to represent variables. Letters often used for variables are [latex]x,y,a,b,\\text{ and }c[\/latex].\r\n<div class=\"textbox shaded\">\r\n<h3>Variables and Constants<\/h3>\r\nA variable is a letter that represents a number or quantity whose value may change.\r\nA constant is a number whose value always stays the same.\r\n\r\n<\/div>\r\nTo write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In Whole Numbers, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.\r\n<table class=\"unnumbered\" style=\"width: 40%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\"><strong>Operation<\/strong><\/th>\r\n<th data-align=\"left\"><strong>Notation<\/strong><\/th>\r\n<th data-align=\"left\"><strong>Say:<\/strong><\/th>\r\n<th data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Addition<\/td>\r\n<td data-align=\"left\">[latex]a+b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a\\text{ plus }b[\/latex]<\/td>\r\n<td data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Subtraction<\/td>\r\n<td data-align=\"left\">[latex]a-b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a\\text{ minus }b[\/latex]<\/td>\r\n<td data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Multiplication<\/td>\r\n<td data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a\\text{ times }b[\/latex]<\/td>\r\n<td data-align=\"left\">The product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Division<\/td>\r\n<td data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\r\n<td data-align=\"left\">The quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn algebra, the cross symbol, [latex]\\times [\/latex], is not used to show multiplication because that symbol may cause confusion. Does [latex]3xy[\/latex] mean [latex]3\\times y[\/latex] (three times [latex]y[\/latex] ) or [latex]3\\cdot x\\cdot y[\/latex] (three times [latex]x\\text{ times }y[\/latex] )? To make it clear, use \u2022 or parentheses for multiplication.\r\n\r\nWe perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <em data-effect=\"italics\">of<\/em> or <em data-effect=\"italics\">and<\/em> to help you find the numbers.\r\n<ul id=\"fs-id1969800\" data-labeled-item=\"true\">\r\n \t<li>The <em data-effect=\"italics\">sum\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]5[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]3[\/latex] means add [latex]5[\/latex] plus [latex]3[\/latex], which we write as [latex]5+3[\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">difference\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]9[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]2[\/latex] means subtract [latex]9[\/latex] minus [latex]2[\/latex], which we write as [latex]9 - 2[\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">product\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]4[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]8[\/latex] means multiply [latex]4[\/latex] times [latex]8[\/latex], which we can write as [latex]4\\cdot 8[\/latex].<\/li>\r\n \t<li>The <em data-effect=\"italics\">quotient\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]20[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]5[\/latex] means divide [latex]20[\/latex] by [latex]5[\/latex], which we can write as [latex]20\\div 5[\/latex].<\/li>\r\n<\/ul>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nTranslate from algebra to words:\r\n<ol>\r\n \t<li>[latex]12+14[\/latex]<\/li>\r\n \t<li>[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/li>\r\n \t<li>[latex]64\\div 8[\/latex]<\/li>\r\n \t<li>[latex]x-y[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15.7812px;\">\r\n<td style=\"height: 15.7812px;\">1.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12+14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12[\/latex] plus [latex]14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">the sum of twelve and fourteen<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]30[\/latex] times [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">the product of thirty and five<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]64\\div 8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">[latex]64[\/latex] divided by [latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15.5625px;\">\r\n<td style=\"height: 15.5625px;\">4.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x-y[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x[\/latex] minus [latex]y[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px;\" data-align=\"center\">the difference of [latex]x[\/latex] and [latex]y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144651&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"330\"><\/iframe>\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144652&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\nWhen two quantities have the same value, we say they are equal and connect them with an <em data-effect=\"italics\">equal sign<\/em>.\r\n<div class=\"textbox shaded\">\r\n<h3>Equality Symbol<\/h3>\r\n[latex]a=b[\/latex] is read [latex]a[\/latex] is equal to [latex]b[\/latex]\r\nThe symbol [latex]=[\/latex] is called the equal sign.\r\n\r\n<\/div>\r\nAn inequality is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that [latex]b[\/latex] is greater than [latex]a[\/latex], it means that [latex]b[\/latex] is to the right of [latex]a[\/latex] on the number line. We use the symbols [latex]\\text{&lt;}[\/latex] and [latex]\\text{&gt;}[\/latex] for inequalities.\r\n<p style=\"text-align: center;\">[latex]a&lt;b[\/latex] is read [latex]a[\/latex] is less than [latex]b[\/latex]\r\n[latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line<\/p>\r\n<p style=\"text-align: center;\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215726\/CNX_BMath_Figure_02_01_001.png\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/png\" \/>\r\n[latex]a&gt;b[\/latex] is read [latex]a[\/latex] is greater than [latex]b[\/latex]\r\n[latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215727\/CNX_BMath_Figure_02_01_002.png\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/png\" \/>\r\n\r\nThe expressions [latex]a&lt;b\\text{ and }a&gt;b[\/latex] can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}a&lt;b\\text{ is equivalent to }b&gt;a.\\text{ For example, }7&lt;11\\text{ is equivalent to }11&gt;7.\\hfill \\\\ a&gt;b\\text{ is equivalent to }b&lt;a.\\text{ For example, }17&gt;4\\text{ is equivalent to }4&lt;17.\\hfill \\end{array}[\/latex]<\/p>\r\nWhen we write an inequality symbol with a line under it, such as [latex]a\\le b[\/latex], it means [latex]a&lt;b[\/latex] or [latex]a=b[\/latex]. We read this [latex]a[\/latex] is less than or equal to [latex]b[\/latex]. Also, if we put a slash through an equal sign, [latex]\\ne[\/latex], it means not equal.\r\n\r\nWe summarize the symbols of equality and inequality in the table below.\r\n<table style=\"width: 40%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Algebraic Notation<\/th>\r\n<th data-align=\"center\">Say<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a=b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\ne b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is not equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a&lt;b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is less than [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a&gt;b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is greater than [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\le b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is less than or equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\ge b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is greater than or equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n<h3 style=\"text-align: left;\">Symbols [latex]&amp;lt[\/latex] and [latex]&amp;gt[\/latex]<\/h3>\r\n<p style=\"text-align: left;\">The symbols [latex]&amp;lt[\/latex] and [latex]&amp;gt[\/latex] each have a smaller side and a larger side.<\/p>\r\n<p style=\"text-align: center;\">smaller side [latex]&amp;lt[\/latex] larger side<\/p>\r\n<p style=\"text-align: center;\">larger side [latex]&amp;gt[\/latex] smaller side<\/p>\r\nThe smaller side of the symbol faces the smaller number and the larger faces the larger number.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nTranslate from algebra to words:\r\n<ol>\r\n \t<li>[latex]20\\le 35[\/latex]<\/li>\r\n \t<li>[latex]11\\ne 15 - 3[\/latex]<\/li>\r\n \t<li>[latex]9&gt;10\\div 2[\/latex]<\/li>\r\n \t<li>[latex]x+2&lt;10[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"346424\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"346424\"]\r\n\r\nSolution:\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]20\\le 35[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]20[\/latex] is less than or equal to [latex]35[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11\\ne 15 - 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]11[\/latex] is not equal to [latex]15[\/latex] minus [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]9&gt;10\\div 2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]9[\/latex] is greater than [latex]10[\/latex] divided by [latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]x+2&lt;10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]x[\/latex] plus [latex]2[\/latex] is less than [latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php? id=144653&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<iframe id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144654&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144655&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">In the following video we show more examples of how to write inequalities as words.<\/span>\r\n\r\nhttps:\/\/youtu.be\/q2ciQBwkjbk\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nThe information in the table below compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol [latex]\\text{=},\\text{&lt;},\\text{ or }\\text{&gt;}[\/latex] in each expression to compare the fuel economy of the cars.\r\n\r\n(credit: modification of work by Bernard Goldbach, Wikimedia Commons)\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215729\/CNX_BMath_Figure_02_01_003.png\" alt=\"This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled \" data-media-type=\"image\/png\" \/>\r\n<ol>\r\n \t<li>MPG of Prius_____ MPG of Mini Cooper<\/li>\r\n \t<li>MPG of Versa_____ MPG of Fit<\/li>\r\n \t<li>MPG of Mini Cooper_____ MPG of Fit<\/li>\r\n \t<li>MPG of Corolla_____ MPG of Versa<\/li>\r\n \t<li>MPG of Corolla_____ MPG of Prius<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"826680\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"826680\"]\r\n\r\nSolution\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Prius____MPG of Mini Cooper<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the values in the chart.<\/td>\r\n<td data-align=\"center\">48____27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare.<\/td>\r\n<td data-align=\"center\">48 &gt; 27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Prius &gt; MPG of Mini Cooper<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Versa____MPG of Fit<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the values in the chart.<\/td>\r\n<td data-align=\"center\">26____27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare.<\/td>\r\n<td data-align=\"center\">26 &lt; 27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Versa &lt; MPG of Fit<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Mini Cooper____MPG of Fit<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the values in the chart.<\/td>\r\n<td data-align=\"center\">27____27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare.<\/td>\r\n<td data-align=\"center\">27 = 27<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Mini Cooper = MPG of Fit<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Corolla____MPG of Versa<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the values in the chart.<\/td>\r\n<td data-align=\"center\">28____26<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare.<\/td>\r\n<td data-align=\"center\">28 &gt; 26<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Corolla &gt; MPG of Versa<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"width: 40%;\">\r\n<tbody>\r\n<tr>\r\n<td>5.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Corolla____MPG of Prius<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the values in the chart.<\/td>\r\n<td data-align=\"center\">28____48<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare.<\/td>\r\n<td data-align=\"center\">28 &lt; 48<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-align=\"center\">MPG of Corolla &lt; MPG of Prius<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n<iframe id=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144729&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nGrouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.\r\n<table style=\"width: 40%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th style=\"width: 93.6508%;\" colspan=\"2\" data-align=\"center\"><strong>Common Grouping Symbols<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"width: 61.4286%;\" data-align=\"left\">parentheses<\/td>\r\n<td style=\"width: 32.2222%;\" data-align=\"center\">( )<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 61.4286%;\" data-align=\"left\">brackets<\/td>\r\n<td style=\"width: 32.2222%;\" data-align=\"center\">[ ]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 61.4286%;\" data-align=\"left\">braces<\/td>\r\n<td style=\"width: 32.2222%;\" data-align=\"center\">{ }<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nHere are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{cc}8\\left(14 - 8\\right)21 - 3\\\\\\left[2+4\\left(9 - 8\\right)\\right]\\\\24\\div \\left\\{13 - 2\\left[1\\left(6 - 5\\right)+4\\right]\\right\\}\\end{array}[\/latex]<\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use variables to represent unknown quantities in algebraic expressions<\/li>\n<li>Identify the variables and constants in an algebraic expression<\/li>\n<li>Use words and symbols to represent algebraic operations on variables and constants<\/li>\n<li>Use inequality symbols to compare two quantities<\/li>\n<li>Translate between words and inequality notation<\/li>\n<\/ul>\n<\/div>\n<h2 data-type=\"title\">Use Variables and Algebraic Symbols<\/h2>\n<p>Greg and Alex have the same birthday, but they were born in different years. This year Greg is [latex]20[\/latex] years old and Alex is [latex]23[\/latex], so Alex is [latex]3[\/latex] years older than Greg. When Greg was [latex]12[\/latex], Alex was [latex]15[\/latex]. When Greg is [latex]35[\/latex], Alex will be [latex]38[\/latex]. No matter what Greg\u2019s age is, Alex\u2019s age will always be [latex]3[\/latex] years more, right?<\/p>\n<p>In the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are variable and the three is a constant. The ages change, or vary, so age is a variable. The [latex]3[\/latex] years between them always stays the same, so the age difference is the constant.<\/p>\n<p>In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age [latex]g[\/latex]. Then we could use [latex]g+3[\/latex] to represent Alex\u2019s age. See the table below.<\/p>\n<table style=\"width: 40%;\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Greg\u2019s age<\/th>\n<th data-align=\"center\">Alex\u2019s age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]12[\/latex]<\/td>\n<td data-align=\"center\">[latex]15[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]20[\/latex]<\/td>\n<td data-align=\"center\">[latex]23[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]35[\/latex]<\/td>\n<td data-align=\"center\">[latex]38[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]g[\/latex]<\/td>\n<td data-align=\"center\">[latex]g+3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Letters are used to represent variables. Letters often used for variables are [latex]x,y,a,b,\\text{ and }c[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>Variables and Constants<\/h3>\n<p>A variable is a letter that represents a number or quantity whose value may change.<br \/>\nA constant is a number whose value always stays the same.<\/p>\n<\/div>\n<p>To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In Whole Numbers, we introduced the symbols for the four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.<\/p>\n<table class=\"unnumbered\" style=\"width: 40%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\"><strong>Operation<\/strong><\/th>\n<th data-align=\"left\"><strong>Notation<\/strong><\/th>\n<th data-align=\"left\"><strong>Say:<\/strong><\/th>\n<th data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\">[latex]a+b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a\\text{ plus }b[\/latex]<\/td>\n<td data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\">[latex]a-b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a\\text{ minus }b[\/latex]<\/td>\n<td data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\n<td data-align=\"left\">[latex]a\\text{ times }b[\/latex]<\/td>\n<td data-align=\"left\">The product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\n<td data-align=\"left\">The quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In algebra, the cross symbol, [latex]\\times[\/latex], is not used to show multiplication because that symbol may cause confusion. Does [latex]3xy[\/latex] mean [latex]3\\times y[\/latex] (three times [latex]y[\/latex] ) or [latex]3\\cdot x\\cdot y[\/latex] (three times [latex]x\\text{ times }y[\/latex] )? To make it clear, use \u2022 or parentheses for multiplication.<\/p>\n<p>We perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <em data-effect=\"italics\">of<\/em> or <em data-effect=\"italics\">and<\/em> to help you find the numbers.<\/p>\n<ul id=\"fs-id1969800\" data-labeled-item=\"true\">\n<li>The <em data-effect=\"italics\">sum\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]5[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]3[\/latex] means add [latex]5[\/latex] plus [latex]3[\/latex], which we write as [latex]5+3[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">difference\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]9[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]2[\/latex] means subtract [latex]9[\/latex] minus [latex]2[\/latex], which we write as [latex]9 - 2[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">product\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]4[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]8[\/latex] means multiply [latex]4[\/latex] times [latex]8[\/latex], which we can write as [latex]4\\cdot 8[\/latex].<\/li>\n<li>The <em data-effect=\"italics\">quotient\u00a0<\/em><strong><em data-effect=\"italics\">of<\/em><\/strong> [latex]20[\/latex] <strong><em data-effect=\"italics\">and<\/em><\/strong> [latex]5[\/latex] means divide [latex]20[\/latex] by [latex]5[\/latex], which we can write as [latex]20\\div 5[\/latex].<\/li>\n<\/ul>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Translate from algebra to words:<\/p>\n<ol>\n<li>[latex]12+14[\/latex]<\/li>\n<li>[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/li>\n<li>[latex]64\\div 8[\/latex]<\/li>\n<li>[latex]x-y[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15.7812px;\">\n<td style=\"height: 15.7812px;\">1.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12+14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]12[\/latex] plus [latex]14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">the sum of twelve and fourteen<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]\\left(30\\right)\\left(5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]30[\/latex] times [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the product of thirty and five<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]64\\div 8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">[latex]64[\/latex] divided by [latex]8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" style=\"width: 40%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15.5625px;\">\n<td style=\"height: 15.5625px;\">4.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x-y[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">[latex]x[\/latex] minus [latex]y[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px;\" data-align=\"center\">the difference of [latex]x[\/latex] and [latex]y[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144651&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"330\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144652&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>When two quantities have the same value, we say they are equal and connect them with an <em data-effect=\"italics\">equal sign<\/em>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Equality Symbol<\/h3>\n<p>[latex]a=b[\/latex] is read [latex]a[\/latex] is equal to [latex]b[\/latex]<br \/>\nThe symbol [latex]=[\/latex] is called the equal sign.<\/p>\n<\/div>\n<p>An inequality is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that [latex]b[\/latex] is greater than [latex]a[\/latex], it means that [latex]b[\/latex] is to the right of [latex]a[\/latex] on the number line. We use the symbols [latex]\\text{<}[\/latex] and [latex]\\text{>}[\/latex] for inequalities.<\/p>\n<p style=\"text-align: center;\">[latex]a<b[\/latex] is read [latex]a[\/latex] is less than [latex]b[\/latex]\n[latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215726\/CNX_BMath_Figure_02_01_001.png\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/png\" \/><br \/>\n[latex]a>b[\/latex] is read [latex]a[\/latex] is greater than [latex]b[\/latex]<br \/>\n[latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215727\/CNX_BMath_Figure_02_01_002.png\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/png\" \/><\/p>\n<p>The expressions [latex]a<b\\text{ and }a>b[\/latex] can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}a<b\\text{ is equivalent to }b>a.\\text{ For example, }7<11\\text{ is equivalent to }11>7.\\hfill \\\\ a>b\\text{ is equivalent to }b<a.\\text{ For example, }17>4\\text{ is equivalent to }4<17.\\hfill \\end{array}[\/latex]<\/p>\n<p>When we write an inequality symbol with a line under it, such as [latex]a\\le b[\/latex], it means [latex]a<b[\/latex] or [latex]a=b[\/latex]. We read this [latex]a[\/latex] is less than or equal to [latex]b[\/latex]. Also, if we put a slash through an equal sign, [latex]\\ne[\/latex], it means not equal.\n\nWe summarize the symbols of equality and inequality in the table below.\n\n\n<table style=\"width: 40%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Algebraic Notation<\/th>\n<th data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a=b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\ne b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is not equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a<b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is less than [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a>b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is greater than [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\le b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is less than or equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\ge b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is greater than or equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<h3 style=\"text-align: left;\">Symbols [latex]&lt[\/latex] and [latex]&gt[\/latex]<\/h3>\n<p style=\"text-align: left;\">The symbols [latex]&lt[\/latex] and [latex]&gt[\/latex] each have a smaller side and a larger side.<\/p>\n<p style=\"text-align: center;\">smaller side [latex]&lt[\/latex] larger side<\/p>\n<p style=\"text-align: center;\">larger side [latex]&gt[\/latex] smaller side<\/p>\n<p>The smaller side of the symbol faces the smaller number and the larger faces the larger number.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Translate from algebra to words:<\/p>\n<ol>\n<li>[latex]20\\le 35[\/latex]<\/li>\n<li>[latex]11\\ne 15 - 3[\/latex]<\/li>\n<li>[latex]9>10\\div 2[\/latex]<\/li>\n<li>[latex]x+2<10[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q346424\">Show Solution<\/span><\/p>\n<div id=\"q346424\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]20\\le 35[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]20[\/latex] is less than or equal to [latex]35[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]11\\ne 15 - 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]11[\/latex] is not equal to [latex]15[\/latex] minus [latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td>[latex]9>10\\div 2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]9[\/latex] is greater than [latex]10[\/latex] divided by [latex]2[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<\/tr>\n<tr>\n<td>[latex]x+2<10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]x[\/latex] plus [latex]2[\/latex] is less than [latex]10[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php? id=144653&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144654&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144655&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<p><span style=\"color: #000000;\">In the following video we show more examples of how to write inequalities as words.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Write Inequalities as Words\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/q2ciQBwkjbk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>The information in the table below compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol [latex]\\text{=},\\text{<},\\text{ or }\\text{>}[\/latex] in each expression to compare the fuel economy of the cars.<\/p>\n<p>(credit: modification of work by Bernard Goldbach, Wikimedia Commons)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215729\/CNX_BMath_Figure_02_01_003.png\" alt=\"This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled\" data-media-type=\"image\/png\" \/><\/p>\n<ol>\n<li>MPG of Prius_____ MPG of Mini Cooper<\/li>\n<li>MPG of Versa_____ MPG of Fit<\/li>\n<li>MPG of Mini Cooper_____ MPG of Fit<\/li>\n<li>MPG of Corolla_____ MPG of Versa<\/li>\n<li>MPG of Corolla_____ MPG of Prius<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q826680\">Show Solution<\/span><\/p>\n<div id=\"q826680\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Prius____MPG of Mini Cooper<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">48____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">48 &gt; 27<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Prius &gt; MPG of Mini Cooper<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Versa____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">26____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">26 &lt; 27<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Versa &lt; MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Mini Cooper____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">27____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">27 = 27<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Mini Cooper = MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Corolla____MPG of Versa<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">28____26<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">28 &gt; 26<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Corolla &gt; MPG of Versa<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 40%;\">\n<tbody>\n<tr>\n<td>5.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Corolla____MPG of Prius<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">28____48<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">28 &lt; 48<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">MPG of Corolla &lt; MPG of Prius<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom6\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144729&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.<\/p>\n<table style=\"width: 40%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 93.6508%;\" colspan=\"2\" data-align=\"center\"><strong>Common Grouping Symbols<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 61.4286%;\" data-align=\"left\">parentheses<\/td>\n<td style=\"width: 32.2222%;\" data-align=\"center\">( )<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 61.4286%;\" data-align=\"left\">brackets<\/td>\n<td style=\"width: 32.2222%;\" data-align=\"center\">[ ]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 61.4286%;\" data-align=\"left\">braces<\/td>\n<td style=\"width: 32.2222%;\" data-align=\"center\">{ }<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{cc}8\\left(14 - 8\\right)21 - 3\\\\\\left[2+4\\left(9 - 8\\right)\\right]\\\\24\\div \\left\\{13 - 2\\left[1\\left(6 - 5\\right)+4\\right]\\right\\}\\end{array}[\/latex]<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-6191\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Write Inequalities as Words. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/q2ciQBwkjbk\">https:\/\/youtu.be\/q2ciQBwkjbk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Question ID: 144651, 144652, 144653, 144654, 144655, 144729. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Write Inequalities as Words\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/q2ciQBwkjbk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 144651, 144652, 144653, 144654, 144655, 144729\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"d130a620-0240-4c9b-b841-898720a5b9e6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6191","chapter","type-chapter","status-publish","hentry"],"part":13769,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/6191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":29,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/6191\/revisions"}],"predecessor-version":[{"id":15086,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/6191\/revisions\/15086"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/13769"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/6191\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=6191"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=6191"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=6191"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=6191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}