{"id":36475,"date":"2017-12-27T18:25:56","date_gmt":"2017-12-27T18:25:56","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=36475"},"modified":"2026-03-26T10:00:35","modified_gmt":"2026-03-26T15:00:35","slug":"inequalities","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/inequalities\/","title":{"rendered":"Solving Multi-Step Inequalities"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_oZR2syn7I98\" 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_oZR2syn7I98\" data-source-videoID=\"oZR2syn7I98\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Solving Multi-Step Inequalities Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Solving Multi-Step Inequalities\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_oZR2syn7I98:hover {cursor:pointer;} img#videoThumbnailImage_oZR2syn7I98 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1129-solving-multi-step-inequalities-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_oZR2syn7I98\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_oZR2syn7I98\" 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 Multi-Step Inequalities\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_oZR2syn7I98\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_oZR2syn7I98\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_oZR2syn7I98\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction UlJ_Function() {\n  var x = document.getElementById(\"UlJ\");\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=\"UlJ_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=\"UlJ\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Equalities\" class=\"smooth-scroll\">Equalities<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Solving_a_Linear_Equation\" class=\"smooth-scroll\">Solving a Linear Equation<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Checking_Your_Work\" class=\"smooth-scroll\">Checking Your Work<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Solve_Inequalities\" class=\"smooth-scroll\">How to Solve Inequalities<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Notation\" class=\"smooth-scroll\">Notation<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Inequality_Problems\" class=\"smooth-scroll\">Inequality Problems<\/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=\"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 review of inequalities! Today, we\u2019ll be looking at what inequalities are and how to solve inequality problems. Let\u2019s get started!<\/p>\n<p>Before we dive into inequalities, let\u2019s remind ourselves what an equality is. <\/p>\n<h2><span id=\"Equalities\" class=\"m-toc-anchor\"><\/span>Equalities<\/h2>\n<p>\nWe know that an \u201cequality,\u201d or an equation, presents values that are equal to each other. An equal sign is the notation that indicates an equation, and it symbolizes the \u201cbalancing\u201d of the expressions on either side. <\/p>\n<p>In order to solve a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/linear-equations\/\">linear equation<\/a>, we use addition, subtraction, multiplication, and division in a specific <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/order-of-operations\/\">order<\/a> to \u201cisolate\u201d the variable on one side of the equation, and a constant on the other side. You have \u201csolved\u201d a linear equation when that variable value is known. It is the one value that, when substituted back into the original equation, will result in a \u201ctrue\u201d statement.<\/p>\n<h3><span id=\"Solving_a_Linear_Equation\" class=\"m-toc-anchor\"><\/span>Solving a Linear Equation<\/h3>\n<p>\nFor a quick review, let\u2019s look at the following example:<\/p>\n<p>Solve the equation for \\(x\\).<\/p>\n<div class=\"examplesentence\">\\(3x-2=x+8\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, we want to get our variables on one side and our constants on another. So I&#8217;m going to add 2 to both sides. That gives us:<\/p>\n<div class=\"examplesentence\">\\(3x=x+10\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, I&#8217;m going to subtract \\(x\\) from this side, and then this side as well (because we want to do the same thing on both sides). That gives us:<\/p>\n<div class=\"examplesentence\">\\(2x=10\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd then to get \\(x\\) by itself divide by 2 on both sides, which gives us:<\/p>\n<div class=\"examplesentence\">\\(x=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe equation states that the expression on the left side of the equal sign, \\(3x-2\\), is equivalent to the expression on the right side, \\(x+8\\). Our goal is to find the one value of \\(x\\) that makes this statement true.<\/p>\n<h3><span id=\"Checking_Your_Work\" class=\"m-toc-anchor\"><\/span>Checking Your Work<\/h3>\n<p>\nSo now we\u2019re going to check our work; what we\u2019re going to do is we\u2019re going to substitute in the 5 for anywhere we see an \\(x\\). <\/p>\n<div class=\"examplesentence\">\\(3(5)-2=15-2=13\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow let\u2019s check it on the other side.<\/p>\n<div class=\"examplesentence\">\\(5+8=13\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd these two values equal each other.<\/p>\n<div class=\"examplesentence\">\\(13=13\\)<\/div>\n<p>\n&nbsp;<br \/>\nA review of these steps is meaningful, because they remain pretty much the same when <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/solving-inequalities-using-all-4-basic-operations\/\">solving inequalities<\/a>. There is a case for some problems that require a small adjustment to the inequality, but we will focus on that later. <\/p>\n<h2><span id=\"How_to_Solve_Inequalities\" class=\"m-toc-anchor\"><\/span>How to Solve Inequalities<\/h2>\n<p>\nIt is important to understand that while solving a linear equation results in one solution, solving an inequality results in a set of <em>many solutions<\/em>. The solving procedure determines the critical value or \u201cboundary\u201d that defines the solution set.<\/p>\n<h3><span id=\"Notation\" class=\"m-toc-anchor\"><\/span>Notation<\/h3>\n<p>\nThe notation of inequalities determines whether or not the critical value that results from the solving process is included or not included in the solution set. Specifically, the symbols <span title=\"less than\"><<\/span> and <span title=\"greater than\">><\/span> define a solution set that does not include the critical value. <\/p>\n<p>This means that the inequality \\(x\\)<\\(10\\) is all the set of numbers less than, but not equal to, 10. Likewise, \\(x\\)>\\(25\\) is the set of all numbers greater than, but not equal to, 25.<\/p>\n<p>We can modify this notation slightly to <em>include<\/em> the critical value that results from the solving process. Note the line under the symbols: \\(\\leq\\) and \\(\\geq\\). Using the previous examples, \\(x\\leq 10\\) is the set of all numbers less than or equal to 10, and \\(x\\geq 25\\) are those numbers greater than or equal to 25.<\/p>\n<p>When inequalities are graphed on a number line, an open circle is used at the critical value to indicate that is NOT included in the solution set, while a closed circle indicates that it is included.<\/p>\n<p>In this example, the closed circle means 4 is included in the solution set:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/01\/inequalities-number-lines-04.svg\" alt=\"\" width=\"460\" height=\"114\" class=\"aligncenter size-full wp-image-211534\"  role=\"img\" \/><\/p>\n<p>In this example, the open circle means -2 is not included in the solution set:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/01\/inequalities-number-lines-05.svg\" alt=\"\" width=\"458\" height=\"114\" class=\"aligncenter size-full wp-image-211537\"  role=\"img\" \/><\/p>\n<p>Let\u2019s sort out this notation with a few examples of solving inequalities. <\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<div class=\"examplesentence\">\\(3x+2 \\leq 17\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe approach here will be the same as solving an equation, but the inequality symbol will be interpreted differently.<\/p>\n<p>The first step to isolate the variable term is to subtract 2 from both sides. This gives us:<\/p>\n<div class=\"examplesentence\">\\(3x \\leq 15\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe second step is to determine the critical value of \\(x\\) by dividing both sides by 3:<\/p>\n<div class=\"examplesentence\">\\(x \\leq 5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe result, \\(x \\leq 5\\), states that all values of <em>x<\/em> that are less than or equal to 5 will satisfy the original inequality.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another one:<\/p>\n<div class=\"examplesentence\">\\(24x-1>99-x\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, the inequality symbol is different in this example, which means that the critical value you will find will not be included in the solution set.<\/p>\n<p>The approach for this multi-step problem is to gather the variable terms to one side, and the constant terms to the other. So we\u2019re going to add 1 to both sides and we\u2019re also going to add <em>x<\/em> to both sides. This gives us:<\/p>\n<div class=\"examplesentence\">\\(25x > 100\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, we&#8217;ll divide both sides by 25. <\/p>\n<div class=\"examplesentence\">\\(x> 4\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis gives us our critical value of 4 because \\(x> 4\\). This final inequality, \\(x> 4\\), tells us that all values of <em>x<\/em> that are greater than but not equal to 4 are in this solution set.<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nAs mentioned, there is a time when you must make an adjustment to the inequality before the solution set is determined. When dividing or multiplying by a negative value in the solving process, it is necessary to reverse the direction of the inequality symbol! This is necessary because sign changes occur with these operations.<\/p>\n<p>The following example illustrates this concept:<\/p>\n<div class=\"examplesentence\">\\( -5x \\geq 20\\)<\/div>\n<p>\n&nbsp;<br \/>\nThere is only one step necessary in this inequality to determine the critical value. Specifically, we need to divide both sides by -5. Because dividing a signed integer results in a sign change, it is also necessary to reverse the direction of the inequality symbol from \\(\\geq\\) to \\(\\leq  \\). So divided by -5 on both sides. Remember to flip your inequality sign and this results in:<\/p>\n<div class=\"examplesentence\">\\(x\\leq -4\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe solution set is all values of <em>x<\/em> that are less than or equal to -4. <\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nLet\u2019s see if you can solve this last example on your own. Be sure to:<\/p>\n<ol>\n<li>Notice the inequality symbol to determine whether the solution set will include or NOT include the critical value<\/li>\n<li>Make sure you change the direction of the inequality symbol if you have to multiply or divide by a negative value in the solving process<\/li>\n<\/ol>\n<div class=\"examplesentence\">\\(-12x+2\\) < \\(-14x -8\\)<\/div>\n<p>\n&nbsp;<br \/>\nPause the video and see what you can come up with.<\/p>\n<p>Okay, let\u2019s solve it together.<\/p>\n<p>Gather the variable terms to one side, and the constant terms to the other. We\u2019re going to subtract 2 from both sides and add \\(14x\\) to both sides. This leaves us with \\(-12x+14x=2x\\) is less than \\(-8-2=-10\\).<\/p>\n<div class=\"examplesentence\">\\(2x\\) < \\(-10\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd then we\u2019re going to divide by 2 on both sides, which gives us \\(x\\) < \\(-5\\).\n\n\nSince we divided by +2 and not -2, we didn&#8217;t have to flip our inequality sign. \n\n\nSo our final solution set is the solution set of all values of \\(x\\) that are less than but NOT equal to -5.\n\n\nI hope this review of inequalities was helpful! Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Inequality_Problems\" class=\"m-toc-anchor\"><\/span>Inequality Problems<\/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 \/>\nWhich of the following inequalities matches the graph below?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Number-line-example-3.svg\" alt=\"A number line with a blue arrow starting at -5 and ending at 3, and a blue-filled circle at 3. The rest of the line from 3 to 5 is black.\" width=\"379\" height=\"40\" class=\"aligncenter size-full wp-image-274231\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(x \\lt 3\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(x \\gt 3\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(x \\geq 3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">\\(x \\leq 3\\)<\/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>The graphed inequality shows a closed circle on the value 3 and an arrow extending to the left. This indicates that the solution set is all values less than or equal to 3. Less than or equal to 3 is expressed as \\(x \\leq 3\\).<\/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 \/>\nSolve the following inequality:<\/p>\n<div class=\"yellow-math-quote\">\\(2x + 3 \\gt 7\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(x \\lt 2\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\\(x \\gt 2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(x \\gt 5\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(x \\lt -5\\)<\/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>Solving an inequality is very similar to solving an equation. The goal is to isolate the variable by using inverse operations.<\/p>\n<p>First, subtract 3 from both sides of the inequality, and then divide both sides by 2. This leaves us with \\(x \\gt 2\\).<\/p>\n<p><em style=\"font-size: 95%\">Note: Only reverse the inequality sign when multiplying or dividing by a negative.<\/em><\/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 \/>\nSolve the following inequality:<\/p>\n<div class=\"yellow-math-quote\">\\(-3x + 5 \\leq -16\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(x \\geq 16\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(x \\geq 7\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(x \\leq 16\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(x \\leq 7\\)<\/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>Once again, the variable needs to be isolated by using inverse operations.<\/p>\n<p>First, subtract 5 from both sides. This gives us \\(-3x \\leq -21\\). From here, divide both sides by \u22123. Remember, when multiplying or dividing by a negative, reverse the inequality sign. Dividing both sides by \u22123 leaves us with \\(x \\geq 7\\).<\/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 \/>\nWhich statement about the graph of the inequality \\(x \\lt -2\\) is incorrect?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\u22122 is a solution to the inequality<\/div><div class=\"PQ\"  id=\"PQ-4-2\">The arrow of the graph will extend to the left<\/div><div class=\"PQ\"  id=\"PQ-4-3\">There will be an open circle on the value \u22122<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\u22123 is a solution to the inequality<\/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>The inequality \\(x \\lt -2\\) is graphed below:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Number-line-example-2.svg\" alt=\"A number line with a blue arrow starting at -2 and extending left through -3 to -4. The circle at -2 is filled, indicating -2 is included.\" width=\"185\" height=\"40\" class=\"aligncenter size-full wp-image-274228\" style=\"margin-top: 2em\" role=\"img\" \/><\/p>\n<p>The arrow reaches to the left of \u22122 because all values that are less than \u22122 are solutions for this inequality. The circle is open because \u22122 itself is not a solution.<\/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 \/>\nSolve the following inequality:<\/p>\n<div class=\"yellow-math-quote\">\\(-3(2x &#8211; 5) + 1 \\geq 4\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x \\geq 2\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(x \\leq\\)<span style=\"font-size: 120%\">\\(\\frac{1}{2}\\)<\/span><\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(x \\leq 2\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x \\leq -2\\)<\/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>For this inequality, isolate the variable using inverse operations.<\/p>\n<p>First, distribute the \u22123 by multiplying it by \\(2x\\) and \u22125. This simplifies to \\(-6x + 15\\).<\/p>\n<p>Now we have \\(-6x + 15 + 1 \\geq 4\\), which simplifies to \\(-6x + 16 \\geq 4\\).<\/p>\n<p>From here, subtract 16 from both sides, and then divide both sides by \u22126. This leaves \\(x \\leq 2\\).<\/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":100243,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-36475","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":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"Solving a mathematical inequality occurs when the equation is solved for the variable in question. 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