Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 6 - Section 6.3 - Equations with Parentheses - Exercises: 47

Answer

y = -1.333333333

Work Step by Step

Simplifying 4(5y + -2) + 3(2y + 6) = 25(3y + 2) + -19y Reorder the terms: 4(-2 + 5y) + 3(2y + 6) = 25(3y + 2) + -19y (-2 * 4 + 5y * 4) + 3(2y + 6) = 25(3y + 2) + -19y (-8 + 20y) + 3(2y + 6) = 25(3y + 2) + -19y Reorder the terms: -8 + 20y + 3(6 + 2y) = 25(3y + 2) + -19y -8 + 20y + (6 * 3 + 2y * 3) = 25(3y + 2) + -19y -8 + 20y + (18 + 6y) = 25(3y + 2) + -19y Reorder the terms: -8 + 18 + 20y + 6y = 25(3y + 2) + -19y Combine like terms: -8 + 18 = 10 10 + 20y + 6y = 25(3y + 2) + -19y Combine like terms: 20y + 6y = 26y 10 + 26y = 25(3y + 2) + -19y Reorder the terms: 10 + 26y = 25(2 + 3y) + -19y 10 + 26y = (2 * 25 + 3y * 25) + -19y 10 + 26y = (50 + 75y) + -19y Combine like terms: 75y + -19y = 56y 10 + 26y = 50 + 56y Solving 10 + 26y = 50 + 56y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-56y' to each side of the equation. 10 + 26y + -56y = 50 + 56y + -56y Combine like terms: 26y + -56y = -30y 10 + -30y = 50 + 56y + -56y Combine like terms: 56y + -56y = 0 10 + -30y = 50 + 0 10 + -30y = 50 Add '-10' to each side of the equation. 10 + -10 + -30y = 50 + -10 Combine like terms: 10 + -10 = 0 0 + -30y = 50 + -10 -30y = 50 + -10 Combine like terms: 50 + -10 = 40 -30y = 40 Divide each side by '-30'. y = -1.333333333 Simplifying y = -1.333333333
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