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3.1 Addition Property of Equality (APE) • Goals: To use the APE to solve equations and word problems The Addition Property of Equality if a = b, then a+c=b+c To solve for “x” x – 8 = 11 • Goal: get “x” alone on one side of the equation. • Do the opposite of whatever is keeping “x” from being all by itself. x – 8 + 8 = 11 + 8 x = 19 Show your work exactly like this: Write the problem: x+7=2 Add same number to -7 -7 both sides of “=“: Write answer with box around it x = -5 y - 8 = -3 +8 +8 y =5 a - 5 = -2 +5 +5 a=3 19 = k + 7 -7 -7 12 = k a + 1.5 = 3 -1.5 -1.5 a = 1.5 1 3 x 2 2 1 1 3 1 x 2 2 2 2 3 1 x 2 2 4 2 2 3 1 x 4 4 3 3 1 3 x 4 4 4 4 1 3 4 1 2 2 m 9 2 2 m 9 9 2 3 6 2 9 9 4 m 9 3 1 x 8 4 3 3 2 3 x 8 8 8 8 5 x 8 A number is increased by 36 is 15. Find the number. Let x = the original number. x + 36 = 15 - 36 - 36 x = -21 A number decreased by 83 is 46. Find the number. Let x = the original number. x - 83 = 46 +83 +83 x = 129 The weekly rent on an apartment was increased by $82. The new rental cost is $675. What is the previous rent? Let x = the previous rent. x + 82 = 675 - 82 - 82 x = 593 Assignment Page 116 (2-40) even Must write problem and show adding same amount to both sides of equal, then the solution.