{"id":6343,"date":"2013-09-29T04:11:53","date_gmt":"2013-09-29T04:11:53","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6343"},"modified":"2014-12-02T08:26:58","modified_gmt":"2014-12-02T08:26:58","slug":"review-of-open-sentences-in-mathematics","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/review-of-open-sentences-in-mathematics\/","title":{"rendered":"Review of Open Sentences in Mathematics"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Open sentences in mathematics are sentences that contain variables.\u00a0 They can be true or false depending upon the numbers that are substituted for the variables.\u00a0 Solving open sentences to make them true is an important part of algebra.<\/p>\n<p><strong>What Are Numerical Expressions?<\/strong><\/p>\n<p>Numerical expressions contain numbers only, such as 4\/5, 2 + 4 = 6, 3 X 2 -1, and so forth.\u00a0 These are closed sentences, and are either always true (such as 2 + 4 =6) or always untrue (as 3 +1 =5).\u00a0 They are evaluated by means of arithmetic.<\/p>\n<p><strong>What Are Variables?<\/strong><\/p>\n<p>Variables are values represented by letters within a number sentence.\u00a0 For example, 3 +y =10 contains the variable y, and l \u2219w=a, contains variables l, w, and a.\u00a0 The integer that equals y in the first sentence is 7, but many numbers can be substituted for l and w.\u00a0 Variables are used in algebraic expressions.<\/p>\n<p><strong>What Are Equations?<\/strong><\/p>\n<p>Equations are number sentences that contain the equals sign, whether or not they contain variables.\u00a0 For example, 2 X 2 = 4 is an equation, as is 14-2 = 12.\u00a0 Sentences such as 2 + x =5 or 3y<sup>2<\/sup> +4 =x are also equations.\u00a0 Sentences do not have to be true to be equations.\u00a0 For example, a sentence like 2 + 2 = 5 is an equation, even though it is false.<\/p>\n<p><strong>What Are Inequalities?<\/strong><\/p>\n<p>Inequalities are number sentences that contain symbols such as &lt; (less than) or &gt; (greater than).\u00a0 Sentences that contain them can also be open sentences, even though there is more than one value that will make the sentence true.\u00a0 For example, the sentence y &gt; 5 can be solved with an infinite set of numbers.\u00a0 False values for the sentence are also an infinite set of numbers.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/math-tutoring\/\">math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/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 Roanoke, VA visit<a href=\"https:\/\/schooltutoring.com\/tutoring-in-roanoke-virginia\/\">: Tutoring in Roanoke, VA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Open sentences in mathematics are sentences that contain variables.\u00a0 They can be true or false depending upon the numbers that are substituted for the variables.\u00a0 Solving open sentences to make them true is an important part of algebra. What Are Numerical Expressions? Numerical expressions contain numbers only, such as 4\/5, 2 + 4 = [&hellip;]<\/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":[13],"tags":[78,936,1246,1926],"class_list":["post-6343","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-algebraic-expressions","tag-inequalities","tag-open-sentences","tag-variables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6343","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=6343"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6343\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}