{"id":648,"date":"2013-05-14T08:24:37","date_gmt":"2013-05-14T08:24:37","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=648"},"modified":"2026-03-25T15:17:39","modified_gmt":"2026-03-25T20:17:39","slug":"equations-and-inequalities","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/equations-and-inequalities\/","title":{"rendered":"Solving Equations and Inequalities"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_7Qx2ty1PQPY\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_7Qx2ty1PQPY\" data-source-videoID=\"7Qx2ty1PQPY\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Solving Equations and Inequalities Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Solving Equations and Inequalities\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_7Qx2ty1PQPY:hover {cursor:pointer;} img#videoThumbnailImage_7Qx2ty1PQPY {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/694-equations-and-inequalities-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_7Qx2ty1PQPY\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_7Qx2ty1PQPY\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Solving Equations and Inequalities\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_7Qx2ty1PQPY\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_7Qx2ty1PQPY\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_7Qx2ty1PQPY\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 5td_Function() {\n  var x = document.getElementById(\"5td\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"5td_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"5td\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_an_Equation\" class=\"smooth-scroll\">What is an Equation?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Algebraic_Expressions\" class=\"smooth-scroll\">Algebraic Expressions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Inequalities\" class=\"smooth-scroll\">Inequalities<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Equations_vs_Inequalities\" class=\"smooth-scroll\">Equations vs. Inequalities<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Equations_and_Inequalities_Practice_Questions\" class=\"smooth-scroll\">Equations and Inequalities Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this Mometrix video on equations and inequalities.<\/p>\n<p>In this video, we\u2019ll talk about  their similarities and differences, what they mean, and we\u2019ll break down, in a way that\u2019s easy to understand, the sometimes confusing inequality signs.<\/p>\n<h2><span id=\"What_is_an_Equation\" class=\"m-toc-anchor\"><\/span>What is an Equation?<\/h2>\n<p>\nSo let\u2019s start with a basic question: What\u2019s an equation?<\/p>\n<p>Here\u2019s a very simple way to think of an equation. An equation has an \u201cequals\u201d sign, like this: \\(2 + 2 = 4\\).<\/p>\n<p>When you see an equals sign, you know that math problem is an equation. It is saying that two or more things are equal. Those \u201cthings\u201d can be simple or complex.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nHere\u2019s an example of a simple equation: \\(10 + 2 = 6 + 6\\).<\/p>\n<p>As you can see, the answer on both sides of the equals sign is 12. The equation says that the sum of the numbers on the left side (\\(10\\div 2\\)) equals the sum of the numbers on the right side (\\(6+6\\)). <\/p>\n<p>Equations can be complex, but at their core, either side of the equals sign remains true. <\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s break down this more complex equation, using this example as a base.<\/p>\n<div class=\"examplesentence\">\\(5 \\times 2 \\div 2 + 10 + 2 = 5 \\times 2 \\div 2 + 6 + 6\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe answer on both sides of the equation is 17. <\/p>\n<p>Let\u2019s break it down.<\/p>\n<div class=\"examplesentence\">\\(5 \\times 2 = 10\\)<br \/>\n\\(10 \\div 2 = 5\\)<br \/>\n\\(5 + 10 + 2 = 17\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd on the other side:<\/p>\n<div class=\"examplesentence\">\\(5 \\times 2 = 10\\)<br \/>\n\\(10 \\div 2 = 5\\)<br \/>\n\\(5 + 6 + 6 = 17\\)<\/div>\n<p>\n&nbsp;<br \/>\nThat\u2019s a simple look at equations.<\/p>\n<h2><span id=\"Algebraic_Expressions\" class=\"m-toc-anchor\"><\/span>Algebraic Expressions<\/h2>\n<p>\nLet\u2019s look at some key terms regarding algebraic equations:<\/p>\n<p>An algebraic expression is the problem you\u2019re trying to solve. The equation \\(x + 7 = 14\\)  is a simple algebraic expression. These expressions contain numbers, variables, and an arithmetic operation that can be as simple as addition or subtraction or as complex as a square root multiplier. <\/p>\n<p>A term is at least one number or variable multiplied together, though terms can have more than one number of variable. For example, \\(2x \u2013 4x = 20\\). The 2 and the 4 are numbers, while \\(x\\) is the variable.<\/p>\n<p>Coefficients multiply variables. So, let\u2019s take a look at \\(6x\\), which means 6  times the variable \\(x\\). Therefore, the number 6 is the coefficient. <\/p>\n<p>Constants are numbers whose values don\u2019t change. The values are fixed. Let\u2019s look at \\(n + 5 = 9\\). The values 5 and 9 don\u2019t change, so those are the constants. Constants can also be variables that stand in for fixed numbers. <\/p>\n<p>Like terms have the same variables and exponents. So, \\(5xy\\), \\(6xy\\), and \\(9xy\\) are like terms because they all contain \\(xy\\).<\/p>\n<p><a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/exponents\/\">Exponents<\/a> are the simplified method of multiplication.  The 3 in \\(x^3\\)  is an exponent. It\u2019s much easier to write and read this  \\(m^3 + y^3 + n^2\\)  than write and read this:<\/p>\n<div class=\"examplesentence\">\\(m \\times m \\times m + y \\times y \\times y + n \\times n\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Inequalities\" class=\"m-toc-anchor\"><\/span>Inequalities<\/h2>\n<p>\nInequalities also have a large part in algebra. While equations mean two things are equal, inequalities (as you might have guessed) show that things are not equal. These are the five inequality signs:<\/p>\n<table class=\"ATable\" style=\"margin: auto; width: 40%;\">\n<tbody>\n<tr>\n<td>\\(\\gt\\)<\/td>\n<td>Greater than<\/td>\n<\/tr>\n<tr>\n<td>\\(\\lt\\)<\/td>\n<td>Less than<\/td>\n<\/tr>\n<tr>\n<td>\\(\\geq\\)<\/td>\n<td>Greater than or equal to<\/td>\n<\/tr>\n<tr>\n<td>\\(\\leq\\)<\/td>\n<td>Less than or equal to<\/td>\n<\/tr>\n<tr>\n<td>\\(\\neq\\)<\/td>\n<td>Not equal<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<br \/>\nSo, in simple inequality terms, \\(8 \\lt 16\\), \\(15 \\gt 9\\), and \\(6 \\neq 5\\). Expressed algebraically, you might see \\(x  \\gt n + 17\\)<\/p>\n<h2><span id=\"Equations_vs_Inequalities\" class=\"m-toc-anchor\"><\/span>Equations vs. Inequalities<\/h2>\n<p>\nEquations and inequalities are similar in some ways, but pretty different in others.<\/p>\n<p>Let\u2019s start with the similarities. You can multiply and divide numbers in inequalities in almost the same way you can when working with equations. Here\u2019s an easy example:<\/p>\n<div class=\"examplesentence\">\\(9x + 10 \\gt 3x + 4\\)<\/div>\n<p>\n&nbsp;<br \/>\nEquations are true. In other words, the value after the equal sign is absolute. There\u2019s no dispute that \\(10 + 10 = 20\\). With inequalities, there are more possible outcomes since there is an infinite number of possibilities for numbers that are less than and greater than.<\/p>\n<p><a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/real-numbers-and-the-number-line\/\">Negative numbers<\/a> work differently. This is where it gets a little bit complicated. Anytime you use a negative number to multiply or divide an inequality, you have to \u201cflip\u201d the inequality sign to keep the equation true.<\/p>\n<p>For example: \\(4 \\gt 3\\).<\/p>\n<p>Four is greater than three. We know that to be true. So let\u2019s expand on both sides a little bit:<\/p>\n<div class=\"examplesentence\">\\(3 \\times 4 \\gt 3 \\times 3\\)<\/div>\n<p>\n&nbsp;<br \/>\nIn this case, 12 is greater than 9. Once again, that\u2019s true.<\/p>\n<p>But if we multiply with negative numbers, things change a little bit.<\/p>\n<p>Let\u2019s have our equation multiply both sides by \u2013 3: \\(&#8211; 3 \\times 4 \\gt -3 \\times 3\\). The answer becomes \\(-12 \\gt -9\\).<\/p>\n<p>But that\u2019s not right. We know negative 12 isn\u2019t greater than negative 9.<\/p>\n<p>That\u2019s why you have to reverse the inequality. If you don\u2019t, the problem won\u2019t be true. So reversing the inequality results in \\(-12 \\lt -9\\), which is true.<\/p>\n<p>So that\u2019s our look at equations and inequalities in algebraic equations. Equations present a true value while inequalities can have any number of outcomes. <\/p>\n<p>I hope this overview was helpful!<\/p>\n<p>Thanks for watching and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"http:\/\/www.differencebetween.net\/language\/difference-between-inequalities-and-equations\/\"target=\"_blank\">\u201cDifference between Inequalities and Equations | Difference Between.\u201d<\/a><\/li>\n<li><a href=\"https:\/\/www.mathsisfun.com\/definitions\/equation.html\"target=\"_blank\">\u201cEquation Definition (Illustrated Mathematics Dictionary).\u201d<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Arithmetic\"target=\"_blank\">\u201cArithmetic.\u201d 2021. Wikipedia.<\/a><\/li>\n<li><a href=\"https:\/\/www.varsitytutors.com\/hotmath\/hotmath_help\/topics\/parts-of-an-expression\"target=\"_blank\">\u201cParts of an Expression.\u201d<\/a><\/li>\n<li><a href=\"https:\/\/www.mathsisfun.com\/algebra\/definitions.html\"target=\"_blank\">\u201cAlgebra &#8211; Definitions.\u201d 2016. Mathsisfun.com<\/a><\/li>\n<li><a href=\"http:\/\/math.typeit.org\/\"target=\"_blank\">\u201cType Mathematical Symbols &#8211; Online Keyboard.\u201d n.d. Math.typeit.org<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is an equation?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>An equation shows that two expressions are equal to one another. For example, in the equation \\(4x+3=7\\), both \\(4x+3\\) and 7 are equal to each other.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is a linear equation?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A linear equation is any equation that graphs as a line.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is an inequality?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>An inequality is a statement comparing two expressions that do not equal each other. Instead, they use the comparisons less than (<), greater than (>), less than or equal to (\u2264), or greater than or equal to (\u2265).<\/p>\n<p>For example, you could write &#8220;\\(x\\) is greater than three&#8221; like this: \\(x > 3\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you solve inequalities?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To solve inequalities, follow the same steps as with an equation. The order of operations is: parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right.<\/p>\n<p>To isolate a variable, work through this process backwards, starting with addition and subtraction and ending with parentheses. There is only one slight difference. If you multiply or divide by a negative number, you have to flip the inequality sign.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Equations_and_Inequalities_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Equations and Inequalities Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(9\\times3-11+2=24 \\div 2+18 \\div 3\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(18=10\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\(18=18\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(10=10\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(40=18\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Both sides of the equal sign must be the same. Simplify the expressions on either side of the equal sign using the order of operations. <\/p>\n<p>We can start by simplifying the expression to the left of the equal sign. <\/p>\n<p style=\"text-align:center;\">\\(9 \\times 3-11+2\\)<\/p>\n<p>According to the Order of Operations, we must multiply before adding and subtracting. Since \\(9 \\times 3=27\\), rewrite the expression using this product.<\/p>\n<p style=\"text-align:center;\">\\(27-11+2\\)<\/p>\n<p>From here, add or subtract from left to right. Since \\(27-11=16\\), rewrite the expression using 16.<\/p>\n<p style=\"text-align:center;\">\\(16+2\\)<\/p>\n<p>\\(16+2=18\\), so the expression to the left of the equal sign is equal to 18.<\/p>\n<p style=\"text-align:center;\">\\(18\\)<\/p>\n<p>Now we simplify the expression to the right of the equal sign. <\/p>\n<p style=\"text-align:center;\">\\(18=24 \\div 2+18 \\div 3\\)<\/p>\n<p>According to the order of operations, we must divide from left to right before adding. Since \\(24 \\div 2=12\\), rewrite the expression using this quotient.<\/p>\n<p style=\"text-align:center;\">\\(18=12+18\\div 3\\)<\/p>\n<p>Next, divide \\(18\u00f73\\), which equals 6. Rewrite the expression using this quotient.<\/p>\n<p style=\"text-align:center;\">\\(18=12+6\\)<\/p>\n<p>\\(12+6=18\\), so the expression to the right of the equal sign is equal to 18.<\/p>\n<p style=\"text-align:center;\">\\(18=18\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat role is the 4 playing in the algebraic equation shown?<\/p>\n<div class=\"yellow-math-quote\">\\(4x^2-xy-y^2=2\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Exponent<\/div><div class=\"PQ\"  id=\"PQ-2-2\">Constant<\/div><div class=\"PQ\"  id=\"PQ-2-3\">Variable<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">Coefficient<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A coefficient is a number that is placed before a variable to multiply it. Since 4 is adjacent to \\(x\\), it is the coefficient in this equation. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMichelle is working on a school project. She needs to write an inequality to describe the weather forecast for the upcoming week. Wednesday\u2019s temperature will be colder than 30\u00b0F. Which inequality best represents this statement?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(x\\geq30\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(x\\leq30\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(x \\gt 30\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(x \\lt 30\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In the inequalities given, \\(x\\) represents Wednesday\u2019s temperature. The inequality symbol that can be used to represent \u201ccolder than\u201d is the &#8220;less than&#8221; symbol. The inequality that best matches the scenario is \\(x \\lt 30\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nNatasha\u2019s mom gives her $20 to spend at the fair. The fair admission costs $6 and the rides cost $0.25 each. To find out how many rides she can go on, Natasha wrote the following inequality: <\/p>\n<p style=\"text-align:center;\">\\(0.25x+6\\leq20\\)<\/p>\n<p>Based on this inequality, what is the greatest amount of rides Natasha can go on at the fair? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">56 rides<\/div><div class=\"PQ\"  id=\"PQ-4-2\">55 rides <\/div><div class=\"PQ\"  id=\"PQ-4-3\">48 rides <\/div><div class=\"PQ\"  id=\"PQ-4-4\">30 rides <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the answer, solve for \\(x\\) in the inequality.<\/p>\n<p style=\"text-align:center;\">\\(0.25x+6\\leq20\\)<\/p>\n<p>First, isolate the variable by doing inverse operations, starting with addition and subtraction. Since the inverse of adding 6 is subtracting 6, subtract 6 from both sides of the inequality.<\/p>\n<p style=\"text-align:center;\">\\(0.25x+6-6\\leq20-6\\)<\/p>\n<p>The sixes cancel out on the left side of the inequality. Since \\(20-6=14\\), we can rewrite the inequality using 14.<\/p>\n<p style=\"text-align:center;\">\\(0.25\\leq14\\)<\/p>\n<p>Next, we isolate the variable by doing inverse operations again. Since the inverse of multiplying is dividing, divide both sides of the inequality by 0.25.<\/p>\n<p style=\"text-align:center;\">\\(0.25\\div0.25\\leq14\\div0.25\\)<\/p>\n<p>The left side of the inequality cancels out, leaving us with <em>x<\/em>. On the right side, we have \\(14\u00f70.25\\) which equals 56. Therefore, \\(x\\) is less than or equal to 56.<\/p>\n<p>The greatest amount of rides Natasha can go on is 56. <\/p>\n<p style=\"text-align:center;\">\\(x\\leq56\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSimplify the following inequality:<\/p>\n<div class=\"yellow-math-quote\">\\(-4\\times8 \\lt -4\\times9\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(32 \\lt -36\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(-32 \\lt -36\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(-32 \\gt -36\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(-36 \\gt -32\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When multiplying or dividing by a negative number, you must reverse the order of the inequality sign.<\/p>\n<p>Since both sides of this inequality are multiplied by -4, the inequality sign needs to be flipped from less than (<) to greater than (>). \\(-4\\times8=-32\\) and \\(-4\\times9=-36\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":99718,"parent":0,"menu_order":16,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-648","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-inequalities-videos","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/648","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=648"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/648\/revisions"}],"predecessor-version":[{"id":261226,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/648\/revisions\/261226"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99718"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}