{"id":123019,"date":"2022-05-30T11:38:20","date_gmt":"2022-05-30T16:38:20","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=123019"},"modified":"2026-03-28T11:53:13","modified_gmt":"2026-03-28T16:53:13","slug":"solving-one-step-inequalities","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/solving-one-step-inequalities\/","title":{"rendered":"Solving One-Step Inequalities"},"content":{"rendered":"<h1>Solving One-Step Inequalities<\/h1>\n\n\t\t\t<div id=\"mmDeferVideoEncompass_rtcHuVsoEak\" 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_rtcHuVsoEak\" data-source-videoID=\"rtcHuVsoEak\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Solving One-Step Inequalities Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Solving One-Step Inequalities\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_rtcHuVsoEak:hover {cursor:pointer;} img#videoThumbnailImage_rtcHuVsoEak {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2473-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_rtcHuVsoEak\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_rtcHuVsoEak\" 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 One-Step Inequalities\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_rtcHuVsoEak\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_rtcHuVsoEak\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_rtcHuVsoEak\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Welcome to this video on <strong>solving one-step inequalities<\/strong>. This process should look very similar to the process of <a href=\"https:\/\/www.mometrix.com\/academy\/solving-one-step-equations\/\"><strong>solving one-step equations<\/strong><\/a>.<\/p>\n<p>Let\u2019s jump into some examples!<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x+7\\gt -3\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Since the goal, like with solving equations, is to isolate \\(x\\) on one side, we need to get rid of the \\(+7\\) on the left side. We do this by subtracting 7 from both sides, just like with a one-step equation.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x+7-7\\gt -3-7\\)<br \/>\n&nbsp;<br \/>\n\\(x\\gt -10\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>And this is our answer for our inequality. Sometimes when you have one-step inequalities you&#8217;ll be asked to graph your solution. So if you were to graph this solution, it would look something like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-123109\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-e1654014706566.jpg\" alt=\"greater than -10 inequality\" width=\"652\" height=\"122\" \/><\/p>\n<p>Since we have a greater than sign, and not greater than or equal to, \\(\u201310\\) is not in the solution set. We show this with an open circle above \\(\u201310\\).<\/p>\n<p>Let\u2019s try another one! Solve the inequality:<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x-\\leq 23\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>To isolate \\(x\\) on the right side, add 2 to both sides.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x-2+2\\leq 3+2\\)<br \/>\n&nbsp;<br \/>\n\\(x\\leq 5\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now let&#8217;s draw a graph of our solution. Because there is a less than or equal to sign, 5 is included in our answer, and we use a closed dot on our graph.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-2-e1654014739578.jpg\" alt=\"same or less than five inequality\" width=\"652\" height=\"92\" class=\"aligncenter size-full wp-image-123115\" \/><\/p>\n<p>Now let\u2019s try an example where we have to use division.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(-4x\\geq 16\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>To isolate \\(x\\), we will have to divide both sides by \\(\u20134\\).<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(\\frac{-4x}{-4}\\geq \\frac{16}{-4}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>However, before we go forward, I need to tell you of one special rule. When we divide or multiply by a negative number with inequalities, we have to flip our inequality sign. If you don&#8217;t, your answer will be wrong. So here, our answer will be:<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x\\leq -4\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>It&#8217;s very important that you flip your inequality sign when multiplying or dividing by a negative number. Now let&#8217;s graph our answer. Since we have a less than or equal to sign again, we use a closed dot.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-3.jpg\" alt=\"less than negative four inequality\" width=\"597\" height=\"132\" class=\"aligncenter size-full wp-image-123118\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-3.jpg 597w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-3-300x66.jpg 300w\" sizes=\"auto, (max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Let\u2019s work through one more example together.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(\\frac{x}{6}\\lt 1\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>To isolate \\(x\\), we need to multiply both sides by 6.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(6\\cdot \\frac{x}{6}\\leq 16\\)<br \/>\n&nbsp;<br \/>\n\\(x\\lt 6\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Because we multiplied by a positive number, we don\u2019t have to flip our inequality sign. Then we can graph our solution. We&#8217;re gonna draw an open circle above 6 because we have a less than sign, 6 is not included in the solution set.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-4.jpg\" alt=\"less than five inequality\" width=\"733\" height=\"150\" class=\"aligncenter size-full wp-image-123121\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-4.jpg 733w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/05\/Solving-one-step-inequalities-4-300x61.jpg 300w\" sizes=\"auto, (max-width: 733px) 100vw, 733px\" \/><\/p>\n<p>I hope this video on solving one-step inequalities was helpful. Thanks for watching, and happy studying!<\/p>\n<\/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>Solving One-Step Inequalities Return to Algebra I Videos<\/p>\n","protected":false},"author":22,"featured_media":123022,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-123019","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123019","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=123019"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123019\/revisions"}],"predecessor-version":[{"id":286219,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123019\/revisions\/286219"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/123022"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=123019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}