<\/p>\n
Overview:<\/strong><\/p>\n Solving equations in algebra depends on using equivalent sentences until the solution is found.\u00a0 Sentences are equivalent if they have the same solution.\u00a0 For example, sentences such as x +3 = 8 and 2x = 10 are equivalent because in both of them x = 5.<\/p>\n How to Use Equivalent Sentences<\/strong><\/p>\n When solving equations, each sentence is equivalent.\u00a0 Suppose you have the equation x +3 = 8.\u00a0 In the next step, subtract -3 from both sides of the sentence to have the equivalent sentence x +3-3 = 8-3.\u00a0 That means that x = 8-3, or x = 5.\u00a0 The solution to the problem, x=5, is equivalent to the original sentence, x +3 = 8.<\/p>\n Checking for Errors<\/strong><\/p>\n By using equivalent sentences, students can often pinpoint exactly where they went wrong in attempts to solve an equation.\u00a0 For\u00a0 example, suppose the original equation was -6 = y-9.\u00a0 In the next step, -6 + 9 = y-9 + 9, which gives the equivalent sentence -6 + 9 = y.\u00a0 The correct answer is 3 = y.\u00a0 It checks in the original equation, as -6 = 3-9.\u00a0 Suppose that in the second step, a student subtracted the 9 instead of adding the 9 to the -6, to get the solution y =-15.\u00a0 The -15 is not correct in the original equation, as -6 is not equal to ( \u2260 ) -15 – 9.<\/p>\n When Sentences Are Not Equivalent<\/strong><\/p>\n Very often, it is a matter of knowing what sentence cannot be an equivalent solution, because it is not equivalent to the others.\u00a0 In the previous paragraph, x = -15 is not equivalent to the original sentence, -6 = y – 9.\u00a0 Similarly, if x + 3 = 8 and 2x = 10, the equation x -0.4 = 4.96 does not have an equivalent solution, because x -0.4 +0.4 = 4.96 + 0.4 or x = 5.36.\u00a0 The variable x is not equivalent in all three equations if it equals 5 in two of them and 5.36 in one of them.<\/p>\n Equivalent Formulas<\/strong><\/p>\n Students often use formulas to find a solution to an application problem in math.\u00a0 For example, the formula for the area of a rectangle is A = lw, where l is the length and w is the width.\u00a0 Sometimes, one might need to solve the equation for one of the variables instead.\u00a0 When solving for w, the equivalent formula is A\/l = w, and when solving for l the equivalent formula is A\/w = l.<\/p>\n Interested in pre-algebra tutoring services<\/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 Natchez, MS visit: Tutoring in Natchez, MS<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Overview: Solving equations in algebra depends on using equivalent sentences until the solution is found.\u00a0 Sentences are equivalent if they have the same solution.\u00a0 For example, sentences such as x +3 = 8 and 2x = 10 are equivalent because in both of them x = 5. How to Use Equivalent Sentences When solving […]<\/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":[261,596,597],"class_list":["post-6530","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-checking-solutions","tag-equivalent-formulas","tag-equivalent-sentences"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6530","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=6530"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6530\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}