{"id":6432,"date":"2013-11-22T00:16:06","date_gmt":"2013-11-22T00:16:06","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6432"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"solving-equations-with-the-variable-on-both-sides","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/solving-equations-with-the-variable-on-both-sides\/","title":{"rendered":"Solving Equations with the Variable on Both Sides"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

To solve equations with the variable on both sides, move all variables to one side or another.\u00a0 This can be accomplished by using the addition or subtraction principle of equality.\u00a0 Another way to make sure that all the variables are on one side or the other is by removing all grouping symbols.\u00a0 It is much easier to solve the problem when all the variables are on the same side.<\/p>\n

What Are the Equality Properties?<\/strong><\/p>\n

The equality properties of addition or subtraction ensure that the value of the equation does not change.\u00a0 For example, if the equation to solve is 3x +2 = 4x-1, the equality principle of subtraction can be used to move the variables to the same side without changing its value.\u00a0 Subtracting 3x from both sides results in the equation 3x – 3x +2 = 4x-3x -1.\u00a0 Similarly, 3-4x = 10x-10 is the same as 3 -4x +4x = 10x +4x -10 .<\/p>\n

What About Multiplication and Division?<\/strong><\/p>\n

Similarly, the equality properties of multiplication and division also ensure that the value of the equation is unchanged.\u00a0 If the equation is 6x = 3x +18, the equality property of subtraction can first be applied as 6x-3x = 3x-3x +18, or 3x = 18, or 3x\/3 =\u00a0 18\/3, or x = 6.\u00a0 In the same way, 2(x-2) = 3x – (4x-5) can be simplified to 2x – 4 -= -x +5, or 2x +x -4 = x – x +5 or 3x – 4 = 5, or 3x -4 +4 = 5 +4 or 3x = 9, or 3x\/3 = 9\/3 or x = 3.<\/p>\n

What About the Distributive Property?<\/strong><\/p>\n

In order to move all variables from one side to another, sometimes the groupings have to be solved first.\u00a0 For example, a problem such as 2(x-3) +5 = 3(x-1) has groupings on both sides of the equation.\u00a0 Before the variables can all be moved to the same side, both sets of parentheses need to be solved, so that 2x -6 +5 = 3x -3.\u00a0 Then, 2x-2x -1 = 3x-2x -3.\u00a0 In the next step, -1 = x-3, or x =2.\u00a0 To check, does 2 (2-3) +5 equal 3 (2-1)?<\/p>\n

Does the Equation Have More than One Solution?<\/strong><\/p>\n

Occasionally, solving equations will result in more than one solution, or even all numbers as a solution, because both sides of the equation turn out to be equivalent.\u00a0 For example, solve 3 (x +1) -5 = 3x-2.\u00a0 Solving the grouping results in 3x +3-5 = 3x-2 or 3x-2 = 3x-2.\u00a0 The expressions on both sides of the equation are the same.<\/p>\n

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Overview: To solve equations with the variable on both sides, move all variables to one side or another.\u00a0 This can be accomplished by using the addition or subtraction principle of equality.\u00a0 Another way to make sure that all the variables are on one side or the other is by removing all grouping symbols.\u00a0 It is […]<\/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],"tags":[519,587,591],"class_list":["post-6432","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-distributive-property","tag-equality-properties","tag-equations-with-multiple-solutions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6432","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=6432"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6432\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}