Overview:\u00a0 What Are Inequalities?<\/b>
\nMost of the time, in order to solve problems in pre-algebra or algebra, students use equations, where number sentences are exactly equal.\u00a0 However, some number sentences use expressions that are inequalities, such as < (less than), > (greater than), \u2264 (less than or equal to), or \u2265 (greater than or equal to).\u00a0 They are solved by following similar rules to equations, with a few differences.<\/p>\n
Addition and Subtraction Rules for Inequalities<\/b>
\nAddition rules for inequalities are very similar to addition rules for equations.\u00a0 The commutative property for addition holds in a special way.\u00a0 If a>b , then a +c > b +c, and \u00a0a – c> b – c.\u00a0 (Remember that letters stand for the same number or both sides of the sentence.\u00a0 If a =5 , b=4, and c =1, then 5>4, and 5+1 > 4+1.\u00a0 The letters don’t stand for something else in the middle of the problem.<\/p>\n
Is “Less than”\u00a0 Similar to “Greater than”?<\/b>
\nThe rules for less than are similar to the rules for greater than.\u00a0 If a <b, then a +c < b +c and a-c < b-c.<\/p>\n
For example, the number sentence is x-7\u2265-8.\u00a0 Solving for x and using the rules, get x as the only number to the right of the inequality the same way as solving an equation, by adding 7 to each side.\u00a0\u00a0 Therefore, x-7 +7 \u2265 -8 +7, or x-0 \u2265 -1, or x.\u2265-1.<\/p>\n
Multiplication and Division Rules for Inequalities<\/b>
\nMultiplication (and its inverse, division) have similar rules to addition and subtraction.\u00a0 For all numbers a, b, c , if a >b, then a times c > b times c, and a\/c > b\/c.\u00a0 If a<b, then a(c) < b(c), and a\/c < b\/c.\u00a0 To test that in the real world, let a =5, b=4, and c =1, but it will work for any positive real number.\u00a0 For example, 5 >4, so 5(1) > 4(1); and 5\/1 > 4\/1.<\/p>\n
If c is negative, the sign is reversed, because of the rules of multiplication by negative numbers. \u00a0Therefore, for all numbers a, b, and c, if c is negative, if a >b, than a(c) <b(c), and a\/c<b\/c.\u00a0 This time, let a =5, b =4, and c=-2.\u00a0 So, 5>4, but 5(-2) or -10 < 4(-2) or -8. \u00a0\u00a0That is because the larger the negative number is, the further away it is from zero in the opposite direction.<\/p>\n
Graphing Inequalities<\/b>
\nA linear equation will graph as a straight line and will divide the coordinate plane into two regions, one above the\u00a0 line and one below.\u00a0 The only solutions to the equation will fall on the line.\u00a0 However, an inequality will graph as a portion of the coordinate plane.\u00a0 The solutions to the inequality will fall just below the line \u00a0if the number sentence is < (less than) or > (greater than).\u00a0\u00a0 They \u00a0will include the line if \u00a0the number sentence is \u2264 (less than or equal to) or \u2265 (greater than or equal to).<\/p>\n
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Interested in pre-algebra tutoring<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n 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 Boise, ID visit: Tutoring in Boise, ID<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Overview:\u00a0 What Are Inequalities? Most of the time, in order to solve problems in pre-algebra or algebra, students use equations, where number sentences are exactly equal.\u00a0 However, some number sentences use expressions that are inequalities, such as < (less than), > (greater than), \u2264 (less than or equal to), or \u2265 (greater than or equal […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,13],"tags":[50,529,749,936,1159,1186,1366,1762],"class_list":["post-5626","post","type-post","status-publish","format-standard","hentry","category-algebra","category-pre-algebra","tag-addition","tag-division","tag-graphing","tag-inequalities","tag-multiplication","tag-negative-numbers","tag-positive-numbers","tag-subtraction"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5626","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5626"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5626\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}