{"id":9147,"date":"2017-06-11T03:24:16","date_gmt":"2017-06-11T03:24:16","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=9147"},"modified":"2017-07-31T09:52:44","modified_gmt":"2017-07-31T09:52:44","slug":"math-review-of-graphing-compound-inequalities","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-graphing-compound-inequalities\/","title":{"rendered":"Math Review of Graphing Compound Inequalities"},"content":{"rendered":"

Overview<\/h3>\n

Inequalities can be graphed along the number line by solving the inequality and then graphing it.\u00a0 Conjunctions are true when both statements of an inequality are true.\u00a0 Disjunctions are true when either one or both statements of an inequality are true.\u00a0 Both conjunctions and disjunctions can form the basis for truth tables.<\/p>\n

Review of Inequalities and the Number Line<\/h3>\n

Inequalities are expressed by relationships between numbers that are less than <, greater than>, less than or equal to\u2264 or greater than or equal to\u2265.\u00a0 When just one variable is used, the sentence can be represented on the number line.\u00a0 Suppose that a student wanted to show numbers greater than or equal to -40 on the number line.\u00a0 That student might write a sentence such as x is \u2265 -40.\u00a0 Notice that the circle at -40 is filled in as the number -40 makes the inequality a true statement.<\/p>\n

Conjunctions<\/h3>\n

A conjunction is a set of two statements joined by the word \u201cand\u201d, so that both statements must be true.\u00a0 In other words, the points on a number line that are solutions of both inequalities are the solution set.\u00a0 For example, suppose that one inequality is x \u22654 and another inequality is x> 3 +6.\u00a0 The numbers that will be in common are the points larger than 9, but not including 9.\u00a0 Although 9 is greater than 4, it is not included in the second inequality statement.<\/p>\n

<\/h3>\n

Disjunctions<\/h3>\n

A disjunction is a set of two statements joined by the word \u201cor\u201d, so that both statements could be true, or only one statement could be true.\u00a0 Suppose one sentence is x> 3 and the other sentence is x \u2264 0.\u00a0 The points that make that statement true are either those that are greater than 3 or those that are less than or equal to 0.<\/p>\n

<\/h3>\n

Truth Tables<\/h3>\n

Truth tables are another way of organizing statements, and are part of logic and a form of math called discrete math.\u00a0 In a conjunction, a statement is true only if both statements are true.\u00a0 For example, the statement \u201ctwo is a prime number and three is an odd number\u201c is true because both parts of the statement is true.\u00a0 However, the statement \u201ctwo is an odd number and three is a prime number\u201d is false because the first statement is false.\u00a0 Similarly, \u201cFour is an even number and six is an odd number\u201d is false because the second statement is false.\u00a0 \u201cSeven is an even number and four is an odd number\u201d is false because both statements are false.<\/p>\n

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Overview Inequalities can be graphed along the number line by solving the inequality and then graphing it.\u00a0 Conjunctions are true when both statements of an inequality are true.\u00a0 Disjunctions are true when either one or both statements of an inequality are true.\u00a0 Both conjunctions and disjunctions can form the basis for truth tables. Review of […]<\/p>\n","protected":false},"author":22,"featured_media":66893,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[3056,4043,1219,4044],"class_list":["post-9147","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-algebra","tag-conjunctions","tag-disjunctions","tag-number-line","tag-truth-tables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9147","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=9147"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/9147\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media\/66893"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=9147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=9147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=9147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}