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LESSON 3.2 - Solving Equations Using Multiplication or Division Goal: Solve equations using multiplication or division. Warm-up: Solve the equation. Show your steps! 1) x + 6 = -13 4) -4 + x = 15 2) 4 + x = 20 5) x – (-3) = 9 3) x – 9 = -11 6) x + (-5) = 10 Discuss the following two answers with your group and record your thoughts> 7) Why must equations be “balanced”? 8) How can writing algebraic equations make word problems easier to solve? Multiplication Property of Equality Words Multiplying each side of an equation by the same nonzero number produces an equivalent equation. x x Numbers If = 6, then 4= 4 4 4 Algebra If a = b and c 0, then ac = . EXAMPLE 1 - Solving an equation Using Multiplication a) t 8 =6 1 t b) 3 = -12 3 4 x = 24 c) Division property of Equality Words Dividing each side of an equation by the same nonzero number produces an equivalent equation. 3x 21 Numbers If 3x = 21, then = . 3 Algebra If a = b and c 0, then a c = . EXAMPLE 2 - Solving an Equation Using Division a) –8y = 17 b) 3.2x = -16 c) –x = 25 Now You Try It! - Solve the equation. Check your solution. Check! x 1) 14 = 8 2) 3) x 4.5 = 12 56 = –3.5x 2 4) 8x = 72 5) –y = 20 EXAMPLE 3 - Writing and Solving an Equation Pizza Three people equally share the cost of a pizza. The total cost of the pizza is $14.67. Write and solve an equation to find each person’s cost. Solution Let c represent each person’s cost. Number = of people Think: what part of the verbal model is missing? What values correspond to each part of the verbal model? 3