Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 38

Answer

{-33}

Work Step by Step

5x - 4(x + 9) = 2x - 3 Step 1 : Use distributive property 5x - 4.x -4.9 = 2x - 3 x - 36 = 2x - 3 Step 2 : Collect variable terms on one side and constants on the other side. subtract 2x from both the sides x - 36 - 2x = 2x - 3 - 2x -x - 36 = -3 Add 36 on both the sides -x - 36 + 36 = -3 + 36 x = -33 Now we check the proposed solution, -33 , by replacing x with -33 in the original equation. Step 1: the original equation 5x - 4(x + 9) = 2x - 3 Step2: Substitute -33 for x 5.(-33) - 4(-33 +9) = 2(-33) -3 Step 3: Simplify 5.(-33) - 4(-24) = 2(-33) -3 Multiply 5.(-33) = -165, 2.(-33) = -66, 4(-24) = -96 -165 + 96 = -66 -3 Solve - 69 = -69 Since the check results in true statement, we conclude that the solution set of the given equation is {-33}
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