{"id":2370,"date":"2012-08-17T00:03:30","date_gmt":"2012-08-17T00:03:30","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=2370"},"modified":"2014-12-02T08:32:06","modified_gmt":"2014-12-02T08:32:06","slug":"solution-set-of-an-inequality","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/solution-set-of-an-inequality\/","title":{"rendered":"Solution Set of an Inequality"},"content":{"rendered":"<p>A solution set is the set of values which <a href=\"https:\/\/schooltutoring.com\/pricing\/\">satisfy<\/a> a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>Solve <strong>2x + 3 \u2264 7<\/strong>, where <strong>x<\/strong> is a natural number.<\/p>\n<p><em><strong>Solution:<\/strong><\/em><\/p>\n<p><strong>2x + 3 \u2264 7<\/strong><\/p>\n<p>Subtracting 3 from both the sides,<\/p>\n<p><strong>2x \u2264 4<\/strong><\/p>\n<p>Dividing both sides by <strong>2<\/strong>,<\/p>\n<p><strong>x \u2264 2<\/strong><\/p>\n<p>Since\u00a0 x is a natural number,<\/p>\n<p>Solution set = <strong>{1,2}<\/strong>.<\/p>\n<h4>Number line:<\/h4>\n<p>The solutions of an inequality can be represented on a number line which is shown in the following examples.<\/p>\n<p><strong>Example: <\/strong><\/p>\n<p>Represent the solution set of inequality <strong>x + 4 \u2264 8<\/strong>, where \u2018<strong>x<\/strong>\u2019 is a whole number.<\/p>\n<p><em><strong>Solution:<\/strong><\/em><\/p>\n<p>Subtracting <strong>4<\/strong> from both sides of given inequality,<\/p>\n<p><strong>x \u2264 4<\/strong><\/p>\n<p>Since <strong>x<\/strong> is a whole number,<\/p>\n<p>Solution set = <strong>{0,1,2,3,4}<\/strong><\/p>\n<p>Its number line representation is,<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/07\/solutin-inequalities-imeage-1.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2371\" title=\"solutin inequalities imeage 1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/07\/solutin-inequalities-imeage-1.bmp\" alt=\"\" \/><\/a><\/p>\n<p><strong>Example 2:<\/strong><\/p>\n<p>Represent the solution set of inequality -7\u2264 3x+2 \u2264 11, where x is a real number.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Subtracting 2 from the given inequality,<\/p>\n<p>-9\u2264 3x \u2264 9<\/p>\n<p>Dividing the above inequality by 3,<\/p>\n<p>-3 \u2264 x \u2264 3<\/p>\n<p>Since x is a real number,<\/p>\n<p>Solution set = {-3,\u2026.,0,\u2026,3}<\/p>\n<p>Its number line representation is,<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/07\/solutin-inequalities-imeage-2.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2372\" title=\"solutin inequalities imeage 2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/07\/solutin-inequalities-imeage-2.bmp\" alt=\"\" \/><\/a><\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in El Monte visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-el-monte-california\/\">Tutoring in El Monte.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A solution set is the set of values which satisfy a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality. Example: Solve 2x + 3 \u2264 7, where x is a natural number. Solution: 2x + 3 \u2264 7 Subtracting [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[816,839,853,868,2180,2199],"class_list":["post-2370","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-how-do-i-solve-inequalities","tag-how-do-solution-sets-and-inequalities-relate","tag-how-do-you-use-solution-sets","tag-how-is-an-inequality-used","tag-what-is-a-solution-set","tag-what-is-an-inequality"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2370","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=2370"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2370\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=2370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=2370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=2370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}