{"id":3570,"date":"2019-12-31T17:05:03","date_gmt":"2019-12-31T17:05:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3570"},"modified":"2021-02-05T23:49:02","modified_gmt":"2021-02-05T23:49:02","slug":"simplifying-and-evaluating-expressions-with-integers","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-and-evaluating-expressions-with-integers\/","title":{"raw":"Simplifying and Evaluating Expressions With Integers That Use Addition","rendered":"Simplifying and Evaluating Expressions With Integers That Use Addition"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Add and subtract integers<\/li><li>Simplify variable expressions for a given value<\/li><li><span>Evaluate variable expressions with integers<\/span><\/li><\/ul><\/div>Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions with any integers.\n\nFor example, if you want to add [latex]37+\\left(-53\\right)[\/latex], you don\u2019t have to count out [latex]37[\/latex] blue counters and [latex]53[\/latex] red counters.\n\nPicture [latex]37[\/latex] blue counters with [latex]53[\/latex] red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because [latex]53 - 37=16[\/latex], there are [latex]16[\/latex] more negative counters.\n\n<p style=\"text-align: center\">[latex]37+\\left(-53\\right)=-16[\/latex]\n\nLet\u2019s try another one. We\u2019ll add [latex]-74+\\left(-27\\right)[\/latex]. Imagine [latex]74[\/latex] red counters and [latex]27[\/latex] more red counters, so we have [latex]101[\/latex] red counters all together. This means the sum is [latex]\\text{-101.}[\/latex]\n\n<p style=\"text-align: center\">[latex]-74+\\left(-27\\right)=-101[\/latex]\n\nLook again at the results of [latex]-74-\\left(27\\right)[\/latex].\n\n<table id=\"eip-663\" summary=\".\"><caption>Addition of Positive and Negative Integers<\/caption><tbody><tr><td><strong>[latex]5+3[\/latex]<\/strong><\/td><td><strong>[latex]-5+\\left(-3\\right)[\/latex]<\/strong><\/td><\/tr><tr><td>both positive, sum positive<\/td><td>both negative, sum negative<\/td><\/tr><tr><td colspan=\"2\">When the signs are the same, the counters would be all the same color, so add them.<\/td><\/tr><tr><td><strong>[latex]-5+3[\/latex]<\/strong><\/td><td><strong>[latex]5+\\left(-3\\right)[\/latex]<\/strong><\/td><\/tr><tr><td>different signs, more negatives<\/td><td>different signs, more positives<\/td><\/tr><tr><td>Sum negative<\/td><td>sum positive<\/td><\/tr><tr><td colspan=\"2\">When the signs are different, some counters would make neutral pairs; subtract to see how many are left.<\/td><\/tr><\/tbody><\/table><div class=\"textbox exercises\"><h3>Exercises<\/h3>Simplify:\n\n<ol><li>[latex]19+\\left(-47\\right)[\/latex]<\/li><li>[latex]-32+40[\/latex]<\/li><\/ol>Solution:\n1. Since the signs are different, we subtract [latex]19[\/latex] from [latex]47[\/latex]. The answer will be negative because there are more negatives than positives.\n\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}19+\\left(-47\\right)\\\\ -28\\end{array}[\/latex]\n\n2. The signs are different so we subtract [latex]32[\/latex] from [latex]40[\/latex]. The answer will be positive because there are more positives than negatives\n\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}-32+40\\\\ 8\\end{array}[\/latex]\n\n<\/div><strong>Tip:<\/strong> Think of positive numbers as money you have and negative numbers as money you owe.&nbsp; This will help you determine if your answer is positive or negative.&nbsp; (-4) + 7 would be owing $4 and having $7, once you settle up, you still have $3.&nbsp; So the answer would be positive 3.\n\nAnother example is (-3) + (-5).&nbsp; This means you owe $3 and you owe $5, so you owe $8, which would be represented by -8.\n\nIf you have 6 + (-10) and we think in terms of money, you have $6 but you owe $10.&nbsp; Once you settle up, you still owe $4.&nbsp; This gives you an answer of -4.\n\n&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145013&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\n\n\n\n<\/div>&nbsp;\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Simplify: [latex]-14+\\left(-36\\right)[\/latex]\n[reveal-answer q=\"55341\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"55341\"]\n\nSolution:\nSince the signs are the same, we add. The answer will be negative because there are only negatives.\n\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}-14+\\left(-36\\right)\\\\ -50\\end{array}[\/latex]\n\n[\/hidden-answer]\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145014&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\n\n\n\n<\/div>The techniques we have used up to now extend to more complicated expressions. Remember to follow the order of operations.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Simplify: [latex]-5+3\\left(-2+7\\right)[\/latex]\n[reveal-answer q=\"935226\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"935226\"]\n\nSolution:\n\n<table id=\"eip-id1168466125594\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\"><tbody><tr><td><\/td><td>[latex]-5+3\\left(-2+7\\right)[\/latex]<\/td><\/tr><tr><td>Simplify inside the parentheses.<\/td><td>[latex]-5+3\\left(5\\right)[\/latex]<\/td><\/tr><tr><td>Multiply.<\/td><td>[latex]-5+15[\/latex]<\/td><\/tr><tr><td>Add left to right.<\/td><td>[latex]10[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145018&amp;theme=oea&amp;iframe_resize_id=mom3[\/embed]\n\n\n\n<\/div>Watch the following video to see another example of how to simplify an expression that contains integer addition and multiplication.\n\nhttps:\/\/youtu.be\/RJ7uU9HbdqA\n\n<h3>Evaluate Variable Expressions with Integers<\/h3>Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions. In our first example we will evaluate a simple variable expression for a negative value.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Evaluate [latex]x+7\\text{ when}[\/latex]\n\n<ol><li>[latex]x=-2[\/latex]<\/li><li>[latex]x=-11[\/latex]<\/li><\/ol>[reveal-answer q=\"140148\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"140148\"]\n\nSolution:\n\n<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\"><tbody><tr><td>1. Evaluate [latex]x+7[\/latex] when [latex]x=-2[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td><\/td><\/tr><tr><td>Substitute [latex]\\color{red}{-2}[\/latex] for [latex]x[\/latex].<\/td><td>[latex]\\color{red}{-2}+7[\/latex]<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\"><\/table><\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]5[\/latex]<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1168466985462\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 11 for x and has negative 11 plus 7. The third row states simplify and has negative 4.\"><tbody><tr><td>2. Evaluate [latex]x+7[\/latex] when [latex]x=-11[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td>[latex]x+7[\/latex]<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\"><\/table><\/td><\/tr><tr><td>Substitute [latex]\\color{red}{-11}[\/latex] for [latex]x[\/latex].<\/td><td>[latex]\\color{red}{-11}+7[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]-4[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try a similar problem.\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145022&amp;theme=oea&amp;iframe_resize_id=mom4[\/embed]\n\n\n\n<\/div>In the next example, we are give two expressions,[latex]n+1[\/latex], and [latex]-n+1[\/latex]. We will evaluate both for a negative number. This practice will help you learn how to keep track of multiple negative signs in one expression.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>When [latex]n=-5[\/latex], evaluate\n\n<ol><li>[latex]n+1[\/latex]<\/li><li>[latex]-n+1[\/latex]<\/li><\/ol>[reveal-answer q=\"57262\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"57262\"]\n\nSolution:\n\n<table id=\"eip-id1168466711125\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has n plus 1. The second row states substitute negative 5 for n and has negative 5 plus 1. The third row states simplify and has negative 4.\"><tbody><tr><td>1. Evaluate [latex]n+1[\/latex] when [latex]n=-5[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td>[latex]n+1[\/latex]<\/td><\/tr><tr><td>Substitute [latex]\\color{red}{-5}[\/latex] for n.<\/td><td>[latex]\\color{red}{-5}+1[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]-4[\/latex]<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1168468416600\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has four rows. The first row has negative n plus 1. The second row states to substitute negative 5 for n and has a negative sign in front of parentheses containing negative 5, then plus one. The third row states simplify and has 5 plus 1. The fourth row states add and has 6.\"><tbody><tr><td>2. Evaluate [latex]-n+1[\/latex] when [latex]n=-5[\/latex]<\/td><td><\/td><\/tr><tr><td><\/td><td>[latex]-n+1[\/latex]<\/td><\/tr><tr><td>Substitute [latex]\\color{red}{-5}[\/latex] for n.<\/td><td>[latex]-(\\color{red}{-5})+1[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]5+1[\/latex]<\/td><\/tr><tr><td>Add.<\/td><td>[latex]6[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try a similar problem.\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145023&amp;theme=oea&amp;iframe_resize_id=mom5[\/embed]\n\n\n\n<\/div>Next we'll evaluate an expression with two variables, where one of the variables is assigned a negative value.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Evaluate [latex]3a+b[\/latex] when [latex]a=12[\/latex] and [latex]b=-30[\/latex].\n[reveal-answer q=\"400918\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"400918\"]\n\nSolution:\n\n<table id=\"eip-id1168466080012\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has four rows. The first row has 3a plus b. The second row states to substitute 12 for a and negative 30 for b and has 3 multiplied by 12 added to negative 30. The third row states to multiply and has 36 plus negative 30. The fourth row states to add and has 6.\"><tbody><tr><td><\/td><td>[latex]3a+b[\/latex]<\/td><\/tr><tr><td>Substitute [latex]\\color{red}{12}[\/latex] for a and [latex]\\color{blue}{-30}[\/latex] for b.<\/td><td>[latex]3(\\color{red}{12})+(\\color{blue}{-30})[\/latex]<\/td><\/tr><tr><td>Multiply.<\/td><td>[latex]36+(-30)[\/latex]<\/td><\/tr><tr><td>Add.<\/td><td>&nbsp;[latex]6[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try a a similar problem.\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145024&amp;theme=oea&amp;iframe_resize_id=mom6[\/embed]\n\n\n\n<\/div>In the next example, the expression has an exponent as well as parentheses. It is important to remember the order of operations, you will need to simplify inside the parentheses first, then apply the exponent to the result.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Evaluate [latex]{\\left(x+y\\right)}^{2}[\/latex] when [latex]x=-18[\/latex] and [latex]y=24[\/latex].\n[reveal-answer q=\"653990\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"653990\"]\n\nSolution:\nThis expression has two variables. Substitute [latex]-18[\/latex] for [latex]x[\/latex] and [latex]24[\/latex] for [latex]y[\/latex].\n\n<table id=\"eip-id1168466250152\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has 4 rows. The first row has x plus y inside of parentheses raised to the second power. The second row states to substitute negative 18 for x and 24 for y. It is followed by negative 18 plus 24 inside of parentheses raised to the second power. The third row states to add inside the parentheses and has 6 inside of parentheses raised to the second power. The fourth row states to simplify and has 36.\"><tbody><tr><td><\/td><td>[latex]{\\left(x+y\\right)}^{2}[\/latex]<\/td><\/tr><tr><td>Substitute [latex]\\color{red}{-18}[\/latex] for [latex]x[\/latex] and [latex]\\color{blue}{24}[\/latex] for [latex]y[\/latex].<\/td><td>[latex]{\\left(-18+24\\right)}^{2}[\/latex]<\/td><\/tr><tr><td>Add inside the parentheses.<\/td><td>[latex]{\\left(6\\right)}^{2}[\/latex]<\/td><\/tr><tr><td>Simplify<\/td><td>[latex]36[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>Now you can try a similar problem.\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145025&amp;theme=oea&amp;iframe_resize_id=mom7[\/embed]\n\n\n\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add and subtract integers<\/li>\n<li>Simplify variable expressions for a given value<\/li>\n<li><span>Evaluate variable expressions with integers<\/span><\/li>\n<\/ul>\n<\/div>\n<p>Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions with any integers.<\/p>\n<p>For example, if you want to add [latex]37+\\left(-53\\right)[\/latex], you don\u2019t have to count out [latex]37[\/latex] blue counters and [latex]53[\/latex] red counters.<\/p>\n<p>Picture [latex]37[\/latex] blue counters with [latex]53[\/latex] red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because [latex]53 - 37=16[\/latex], there are [latex]16[\/latex] more negative counters.<\/p>\n<p style=\"text-align: center\">[latex]37+\\left(-53\\right)=-16[\/latex]<\/p>\n<p>Let\u2019s try another one. We\u2019ll add [latex]-74+\\left(-27\\right)[\/latex]. Imagine [latex]74[\/latex] red counters and [latex]27[\/latex] more red counters, so we have [latex]101[\/latex] red counters all together. This means the sum is [latex]\\text{-101.}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]-74+\\left(-27\\right)=-101[\/latex]<\/p>\n<p>Look again at the results of [latex]-74-\\left(27\\right)[\/latex].<\/p>\n<table id=\"eip-663\" summary=\".\">\n<caption>Addition of Positive and Negative Integers<\/caption>\n<tbody>\n<tr>\n<td><strong>[latex]5+3[\/latex]<\/strong><\/td>\n<td><strong>[latex]-5+\\left(-3\\right)[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td>both positive, sum positive<\/td>\n<td>both negative, sum negative<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">When the signs are the same, the counters would be all the same color, so add them.<\/td>\n<\/tr>\n<tr>\n<td><strong>[latex]-5+3[\/latex]<\/strong><\/td>\n<td><strong>[latex]5+\\left(-3\\right)[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td>different signs, more negatives<\/td>\n<td>different signs, more positives<\/td>\n<\/tr>\n<tr>\n<td>Sum negative<\/td>\n<td>sum positive<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">When the signs are different, some counters would make neutral pairs; subtract to see how many are left.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Simplify:<\/p>\n<ol>\n<li>[latex]19+\\left(-47\\right)[\/latex]<\/li>\n<li>[latex]-32+40[\/latex]<\/li>\n<\/ol>\n<p>Solution:<br \/>\n1. Since the signs are different, we subtract [latex]19[\/latex] from [latex]47[\/latex]. The answer will be negative because there are more negatives than positives.<\/p>\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}19+\\left(-47\\right)\\\\ -28\\end{array}[\/latex]<\/p>\n<p>2. The signs are different so we subtract [latex]32[\/latex] from [latex]40[\/latex]. The answer will be positive because there are more positives than negatives<\/p>\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}-32+40\\\\ 8\\end{array}[\/latex]<\/p>\n<\/div>\n<p><strong>Tip:<\/strong> Think of positive numbers as money you have and negative numbers as money you owe.&nbsp; This will help you determine if your answer is positive or negative.&nbsp; (-4) + 7 would be owing $4 and having $7, once you settle up, you still have $3.&nbsp; So the answer would be positive 3.<\/p>\n<p>Another example is (-3) + (-5).&nbsp; This means you owe $3 and you owe $5, so you owe $8, which would be represented by -8.<\/p>\n<p>If you have 6 + (-10) and we think in terms of money, you have $6 but you owe $10.&nbsp; Once you settle up, you still owe $4.&nbsp; This gives you an answer of -4.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145013\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145013&#38;theme=oea&#38;iframe_resize_id=ohm145013&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]-14+\\left(-36\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q55341\">Show Solution<\/span><\/p>\n<div id=\"q55341\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nSince the signs are the same, we add. The answer will be negative because there are only negatives.<\/p>\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}-14+\\left(-36\\right)\\\\ -50\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145014\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145014&#38;theme=oea&#38;iframe_resize_id=ohm145014&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The techniques we have used up to now extend to more complicated expressions. Remember to follow the order of operations.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]-5+3\\left(-2+7\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q935226\">Show Solution<\/span><\/p>\n<div id=\"q935226\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466125594\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-5+3\\left(-2+7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td>[latex]-5+3\\left(5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-5+15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add left to right.<\/td>\n<td>[latex]10[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145018\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145018&#38;theme=oea&#38;iframe_resize_id=ohm145018&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another example of how to simplify an expression that contains integer addition and multiplication.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Simplify an Expression With Integers Using the Order of Operations\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/RJ7uU9HbdqA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Evaluate Variable Expressions with Integers<\/h3>\n<p>Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions. In our first example we will evaluate a simple variable expression for a negative value.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]x+7\\text{ when}[\/latex]<\/p>\n<ol>\n<li>[latex]x=-2[\/latex]<\/li>\n<li>[latex]x=-11[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q140148\">Show Solution<\/span><\/p>\n<div id=\"q140148\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\">\n<tbody>\n<tr>\n<td>1. Evaluate [latex]x+7[\/latex] when [latex]x=-2[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-2}[\/latex] for [latex]x[\/latex].<\/td>\n<td>[latex]\\color{red}{-2}+7[\/latex]<\/p>\n<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\"><\/table>\n<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466985462\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 11 for x and has negative 11 plus 7. The third row states simplify and has negative 4.\">\n<tbody>\n<tr>\n<td>2. Evaluate [latex]x+7[\/latex] when [latex]x=-11[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]x+7[\/latex]<\/p>\n<table id=\"eip-id1168466176237\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has x plus 7. The second row states substitute negative 2 for x and has negative 2 plus 7. The third row states simplify and has 5.\"><\/table>\n<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-11}[\/latex] for [latex]x[\/latex].<\/td>\n<td>[latex]\\color{red}{-11}+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145022\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145022&#38;theme=oea&#38;iframe_resize_id=ohm145022&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next example, we are give two expressions,[latex]n+1[\/latex], and [latex]-n+1[\/latex]. We will evaluate both for a negative number. This practice will help you learn how to keep track of multiple negative signs in one expression.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>When [latex]n=-5[\/latex], evaluate<\/p>\n<ol>\n<li>[latex]n+1[\/latex]<\/li>\n<li>[latex]-n+1[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q57262\">Show Solution<\/span><\/p>\n<div id=\"q57262\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466711125\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has three rows. The first row has n plus 1. The second row states substitute negative 5 for n and has negative 5 plus 1. The third row states simplify and has negative 4.\">\n<tbody>\n<tr>\n<td>1. Evaluate [latex]n+1[\/latex] when [latex]n=-5[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]n+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-5}[\/latex] for n.<\/td>\n<td>[latex]\\color{red}{-5}+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468416600\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has four rows. The first row has negative n plus 1. The second row states to substitute negative 5 for n and has a negative sign in front of parentheses containing negative 5, then plus one. The third row states simplify and has 5 plus 1. The fourth row states add and has 6.\">\n<tbody>\n<tr>\n<td>2. Evaluate [latex]-n+1[\/latex] when [latex]n=-5[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-n+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-5}[\/latex] for n.<\/td>\n<td>[latex]-(\\color{red}{-5})+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]5+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145023\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145023&#38;theme=oea&#38;iframe_resize_id=ohm145023&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Next we&#8217;ll evaluate an expression with two variables, where one of the variables is assigned a negative value.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]3a+b[\/latex] when [latex]a=12[\/latex] and [latex]b=-30[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q400918\">Show Solution<\/span><\/p>\n<div id=\"q400918\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466080012\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has four rows. The first row has 3a plus b. The second row states to substitute 12 for a and negative 30 for b and has 3 multiplied by 12 added to negative 30. The third row states to multiply and has 36 plus negative 30. The fourth row states to add and has 6.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3a+b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{12}[\/latex] for a and [latex]\\color{blue}{-30}[\/latex] for b.<\/td>\n<td>[latex]3(\\color{red}{12})+(\\color{blue}{-30})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]36+(-30)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>&nbsp;[latex]6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145024\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145024&#38;theme=oea&#38;iframe_resize_id=ohm145024&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next example, the expression has an exponent as well as parentheses. It is important to remember the order of operations, you will need to simplify inside the parentheses first, then apply the exponent to the result.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]{\\left(x+y\\right)}^{2}[\/latex] when [latex]x=-18[\/latex] and [latex]y=24[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q653990\">Show Solution<\/span><\/p>\n<div id=\"q653990\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThis expression has two variables. Substitute [latex]-18[\/latex] for [latex]x[\/latex] and [latex]24[\/latex] for [latex]y[\/latex].<\/p>\n<table id=\"eip-id1168466250152\" class=\"unnumbered unstyled\" style=\"width: 75%\" summary=\"This figure has 4 rows. The first row has x plus y inside of parentheses raised to the second power. The second row states to substitute negative 18 for x and 24 for y. It is followed by negative 18 plus 24 inside of parentheses raised to the second power. The third row states to add inside the parentheses and has 6 inside of parentheses raised to the second power. The fourth row states to simplify and has 36.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(x+y\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{-18}[\/latex] for [latex]x[\/latex] and [latex]\\color{blue}{24}[\/latex] for [latex]y[\/latex].<\/td>\n<td>[latex]{\\left(-18+24\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add inside the parentheses.<\/td>\n<td>[latex]{\\left(6\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify<\/td>\n<td>[latex]36[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145025\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145025&#38;theme=oea&#38;iframe_resize_id=ohm145025&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-3570\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Simplify an Expression With Integers Using the Order of Operations. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/RJ7uU9HbdqA\">https:\/\/youtu.be\/RJ7uU9HbdqA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 145013, 145014, 145018, 145022, 145023, 145024, 145025. <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":25777,"menu_order":8,"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\":\"cc\",\"description\":\"Ex: Simplify an Expression With Integers Using the Order of Operations\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/RJ7uU9HbdqA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 145013, 145014, 145018, 145022, 145023, 145024, 145025\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3570","chapter","type-chapter","status-web-only","hentry"],"part":1193,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3570","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3570\/revisions"}],"predecessor-version":[{"id":3604,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3570\/revisions\/3604"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1193"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3570\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3570"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3570"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3570"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}