{"id":896,"date":"2013-05-29T07:30:28","date_gmt":"2013-05-29T07:30:28","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=896"},"modified":"2026-03-25T10:48:52","modified_gmt":"2026-03-25T15:48:52","slug":"solving-inequalities-using-all-4-basic-operations","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/solving-inequalities-using-all-4-basic-operations\/","title":{"rendered":"Solving Inequalities Using All 4 Basic Operations"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_xDSHD4UwI5k\" 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_xDSHD4UwI5k\" data-source-videoID=\"xDSHD4UwI5k\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Solving Inequalities Using All 4 Basic Operations Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Solving Inequalities Using All 4 Basic Operations\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_xDSHD4UwI5k:hover {cursor:pointer;} img#videoThumbnailImage_xDSHD4UwI5k {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-solving-inequalities-using-all-4-basic-operations-64c144d1c5cce.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_xDSHD4UwI5k\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_xDSHD4UwI5k\" 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 Inequalities Using All 4 Basic Operations\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_xDSHD4UwI5k\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_xDSHD4UwI5k\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_xDSHD4UwI5k\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction tLo_Function() {\n  var x = document.getElementById(\"tLo\");\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=\"tLo_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=\"tLo\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_an_Inequality\" class=\"smooth-scroll\">What is an Inequality?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Solving_Inequalities\" class=\"smooth-scroll\">Solving Inequalities<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Solving_Inequalities_Practice_Questions\" class=\"smooth-scroll\">Solving 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=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on solving inequalities. In this video, we will discuss:<\/p>\n<ul>\n<li>What an inequality is, and<\/li>\n<li>How to solve inequalities using addition, subtraction, multiplication, and division<\/li>\n<\/ul>\n<h2><span id=\"What_is_an_Inequality\" class=\"m-toc-anchor\"><\/span>What is an Inequality?<\/h2>\n<p>\nWhen solving equations, you have two expressions that are equal to each other. When we look at <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/inequalities\/\">inequalities<\/a>, we are looking at two expressions that are \u201cinequal\u201d or unequal to each other, as the name suggests. This means that one equation will be larger than the other. <\/p>\n<p>The four basic inequalities are: less than, greater than, less than or equal to, and greater than or equal to.<\/p>\n<table class=\"ATable\" style=\"margin: auto; box-shadow: 1.5px 1.5px 3px grey;\">\n<tbody>\n<tr>\n<td height=\"40px\" style=\"text-align: left;\">Less than<\/td>\n<td style=\"border-right: 0px &#038; border-left: 0px\">\n\t\t\t\t< <\/td>\n<\/tr>\n<tr>\n<td height=\"40px\" style=\"text-align: left;\">Less than or equal to<\/td>\n<td style=\"border-right: 0px &#038; border-left: 0px\">\u2264 <\/td>\n<\/tr>\n<tr>\n<td height=\"40px\" style=\"text-align: left;\">Greater than<\/td>\n<td style=\"border-right: 0px &#038; border-left: 0px\">><\/td>\n<\/tr>\n<tr>\n<td height=\"40px\" style=\"text-align: left;\">Greater than or equal to<\/td>\n<td style=\"border-right: 0px &#038; border-left: 0px\">\u2265 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Solving_Inequalities\" class=\"m-toc-anchor\"><\/span>Solving Inequalities<\/h2>\n<p>\nWhen solving inequalities, you follow all the same steps as solving an equation, except for a special rule when it comes to multiplication and division. The main difference is that instead of writing an equal sign between the two expressions, you will write one of the four inequality symbols.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s first look at an inequality using addition.<\/p>\n<div class=\"examplesentence\">\\(x + 7 \\geq 4\\)<\/div>\n<p>\n&nbsp;<br \/>\nIf we are solving for \\(x\\) by itself, we want to get rid of that 7 next to it, so we subtract 7 from both sides.<\/p>\n<div class=\"examplesentence\">\\(x + 7 \u2013 7 \\geq 4 \u2013 7\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis gives us our answer:<\/p>\n<div class=\"examplesentence\">\\(x \\geq -3\\)<\/div>\n<p>\n&nbsp;<br \/>\nIt\u2019s as simple as that!<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nNow, I want you to try one on your own using subtraction.<\/p>\n<div class=\"examplesentence\">\\(x &#8211; 3 \\lt 9\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, we are going to add 3 to both sides.<\/p>\n<div class=\"examplesentence\">\\(x &#8211; 3 + 3 \\lt 9 + 3\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen we simplify.<\/p>\n<div class=\"examplesentence\">\\(x \\lt 12\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nNow we come to multiplication and division.<\/p>\n<p>Are you ready to find out what this special rule is that I was talking about earlier? When you multiply or divide by a negative number, you have to flip your sign the opposite direction. If you are multiplying or dividing by a positive number, don\u2019t worry about this step.<\/p>\n<p>Let\u2019s look at an example:<\/p>\n<div class=\"examplesentence\">\\(-4x \\gt 12\\)<\/div>\n<p>\n&nbsp;<br \/>\nTo get \\(x\\) by itself, we need to divide both sides by -4.<\/p>\n<p>Remember, since we are dividing by -4, we have to flip our inequality sign<\/p>\n<div class=\"examplesentence\">\\(x \\lt -3\\)<\/div>\n<p>\n&nbsp;<br \/>\nLet\u2019s take a second to look at why this happens. What if I didn\u2019t flip my sign? I would have \\(x \\gt -3\\). So let\u2019s try plugging in 2, since 2 is greater than negative 3. If we plug in 2 for \\(x\\), we get:<\/p>\n<div class=\"examplesentence\">\\(-4(2) \\gt 12\\)<br \/>\n\\(-8 > 12\\)\n<\/div>\n<p>\n&nbsp;<br \/>\nBut we know that this isn\u2019t true; -8 is not greater than 12.<\/p>\n<p>Now look back at our correct answer, \\(x \\lt -3\\). Negative 20 is less than negative 3, so let\u2019s plug this into our equation to check and see if it works.<\/p>\n<div class=\"examplesentence\">\\(-4(-20) \\gt 12\\)<br \/>\n\\(80 \\gt 12\\)<\/div>\n<p>\n&nbsp;<br \/>\nThat\u2019s true! 80 is greater than 12. So just remember, when you multiply or divide by a negative number, you HAVE to flip the sign. Otherwise, your inequality will not be true.<\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nWhat if we had this inequality?<\/p>\n<div class=\"examplesentence\">\\(\\frac{x}{3} \\leq 2\\)<\/div>\n<p>\n&nbsp;<br \/>\nFor this inequality, we need to multiply both sides by 3. When we do this, do we flip our sign? No, we don\u2019t have to since we are multiplying by a positive number.<\/p>\n<p>So we\u2019ll multiply both sides by 3, then we get:<\/p>\n<div class=\"examplesentence\">\\(x \\leq 6\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_5\" class=\"m-toc-anchor\"><\/span>Example #5<\/h3>\n<p>\nI want you to try one more on your own. For this one, we are going to combine everything we\u2019ve learned, so it will look a little more challenging, but you can do it. Just apply each step that we have talked about so far.<\/p>\n<div class=\"examplesentence\">\\(2x + 3 \\geq x \u2013 7\\)<\/div>\n<p>\n&nbsp;<br \/>\nPause this video and solve this inequality on your own, then see if your answer matches up with mine.<\/p>\n<p>Think you\u2019ve got it? Let\u2019s see!<\/p>\n<p>First, I\u2019m going to add 7 to both sides of my equation.<\/p>\n<p>This gives us:<\/p>\n<div class=\"examplesentence\">\\(2x + 10 \\geq x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, I have to subtract \\(2x\\) from both sides.<\/p>\n<div class=\"examplesentence\">\\(10 \\geq -x\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, I need to divide by -1 and flip my sign.<\/p>\n<p>So our final answer is:<\/p>\n<div class=\"examplesentence\">\\(-10 \\leq x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, notice with this inequality, you could have subtracted \\(x\\) and subtracted 3 from both sides. This will give you the same answer, and you can avoid dividing by a negative. Sometimes there are multiple ways to solve an inequality or an equation, so be on the lookout for ways to make your life a little bit easier.<\/p>\n<p>I hope this video on solving inequalities was helpful. Thanks for watching and happy studying!<\/p>\n<div style=\"text-align: center;\"><a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/blog\/remembering-the-greater-than-sign-less-than-sign\/\">Greater Than and Less Than Signs<\/a> | <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/multiplication-chart\/\">Multiplication Charts<\/a><\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Solving_Inequalities_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Solving 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 \/>\nSolve the following inequality for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\">\\(4+x \\lt -1-x\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(x \\gt\\)<span style=\"font-size: 120%\">\\(\\: \\frac{1}{2}\\)<\/span><\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(x \\lt 2\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(x \\lt &#8211;\\)<span style=\"font-size: 120%\">\\(\\: \\frac{5}{2}\\)<\/span><\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(x \\gt\\)<span style=\"font-size: 120%\">\\(\\: \\frac{1}{4}\\)<\/span><\/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>To solve this inequality, remember that we need to get \\(x\\) by itself on one side, just like with regular equations.<\/p>\n<p>First, move the 4 to the right side by subtracting 4 from both sides.<\/p>\n<p style=\"text-align:center;\">\n\\(4-4+x \\gt -1-x-4\\)<\/p>\n<p>Simplifying, this leaves us with:<\/p>\n<p style=\"text-align:center;\">\n\\(x \\lt -5-x\\)<\/p>\n<p>Now, we move that \\(-x\\) to the left side by adding it to both sides.<\/p>\n<p style=\"text-align:center;\">\n\\(x+x \\lt -5\\)<br \/>\n\\(2x \\lt -5\\)<\/p>\n<p>Finally, we will divide by 2 on both sides to arrive at the solution. The inequality \\(4+x \\lt -1\u2013x\\) is satisfied whenever \\(x \\lt -\\frac{5}{2}\\).<\/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 for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\"><span style=\"font-size: 120%\">\\(\\frac{x}{4}\\)<\/span>\\(\\:\\geq 3\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(x\\geq12\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(x\\geq4\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(x\\leq12\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(x\\leq3\\)<\/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>To see this, we just need to multiply both sides by 4. This will eliminate the denominator on the left and leave us with \\(x\\) by itself:<\/p>\n<p style=\"text-align:center;\">\n\\(4\\times\\frac{x}{4}\\geq3\\times4\\)<\/p>\n<p>Simplify:<\/p>\n<p style=\"text-align:center;\">\n\\(x\\geq12\\)<\/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 to determine which values of \\(x\\) will satisfy it:<\/p>\n<div class=\"yellow-math-quote\"><span style=\"font-size: 120%\">\\(\\frac{x+2}{7}\\)<\/span>\\(\\: \\gt 2-x\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(x \\gt 5\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(x \\gt\\)<span style=\"font-size: 120%\">\\(\\frac{3}{2}\\)<\/span><\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(x \\lt\\)<span style=\"font-size: 120%\">\\(\\: \\frac{2}{7}\\)<\/span><\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(x \\lt 2\\)<\/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>To begin solving this inequality, let\u2019s eliminate the denominator on the left by multiplying both sides by 7.<\/p>\n<p style=\"text-align: center;\">\n\\(7\\times\\frac{x+2}{7}>(2-x)\\times7\\)<\/p>\n<p>Notice that we have not flipped the inequality sign. That\u2019s because we multiplied by a positive number. The above expression simplifies to:<\/p>\n<p style=\"text-align: center;\">\n\\(x+2>14-7x\\)<\/p>\n<p>From here, we will move the 2 to the right side with subtraction, and move the \\(7x\\) to the left side with addition.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\n\\(x+2-2 \\gt14-7x-2\\)<br \/>\n\\(x \\gt 12-7x\\)<br \/>\n\\(x+7x \\gt 12-7x+7x\\)<br \/>\n\\(8x \\gt 12\\)<\/p>\n<p>Finally, we divide both sides by 8 to get \\(x\\) by itself and we see that we are left with \\(x \\gt 128\\), which simplifies to \\(x \\gt 32\\).<\/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 \/>\nSolve the following inequality for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\">\\(-4x+2\\geq6\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(x\\leq-1\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(x\\geq-1\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(x\\leq2\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(x\\geq2\\)<\/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>Let\u2019s begin working on this problem by subtracting 2 from both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\n\\(-4x+2-2\\geq6-2\\)<br \/>\n\\(-4x\\geq4\\)<\/p>\n<p>Now, in order to isolate \\(x\\) and find the solution, we need to divide both sides by \u22124. Remember, dividing by a negative will flip the inequality sign! This is also true of multiplication by negatives.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\n\\(\\dfrac{-4x}{-4}\\geq\\dfrac{4}{-4}\\)<br \/>\n\\(x\\leq-1\\)<\/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 for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\">\\(&#8211;\\)<span style=\"font-size: 120%\">\\(\\: \\frac{1}{4}\\)<\/span>\\(\\: x+3 \\gt -4\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x \\lt 16\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\(x \\lt 28\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(x \\gt 34\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x \\gt 21\\)<\/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>First, move the 3 to the right-hand side of the inequality by subtracting 3 from both sides.<\/p>\n<p style=\"text-align:center; line-height: 40px\">\n\\(-\\frac{1}{4}x+3-3 \\gt -4-3\\)<br \/>\n\\(-\\frac{1}{4}x \\gt -7\\)<\/p>\n<p>Now, we will get \\(x\\) by itself by multiplying both sides by \u22124. This will cancel the fraction on the left-hand side. This will cause the inequality sign to flip and leave us with our solution after we simplify.<\/p>\n<p style=\"text-align:center; line-height: 40px\">\n\\((-4) \\times -\\frac{1}{4}x \\gt -7 \\times (-4)\\)<br \/>\n\\(x \\lt 28\\)<\/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":187106,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-896","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-inequality-videos","7":"page_category-inequalities-videos","8":"page_category-math-advertising-group","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/896","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=896"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/896\/revisions"}],"predecessor-version":[{"id":278956,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/896\/revisions\/278956"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/187106"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}