## Elementary Technical Mathematics

Published by Brooks Cole

# Chapter 6 - Section 6.3 - Equations with Parentheses - Exercises - Page 242: 54

y=-5

#### Work Step by Step

Simplifying 2(5y + 1) + 16 = 4 + 3(y + -7) Reorder the terms: 2(1 + 5y) + 16 = 4 + 3(y + -7) (1 * 2 + 5y * 2) + 16 = 4 + 3(y + -7) (2 + 10y) + 16 = 4 + 3(y + -7) Reorder the terms: 2 + 16 + 10y = 4 + 3(y + -7) Combine like terms: 2 + 16 = 18 18 + 10y = 4 + 3(y + -7) Reorder the terms: 18 + 10y = 4 + 3(-7 + y) 18 + 10y = 4 + (-7 * 3 + y * 3) 18 + 10y = 4 + (-21 + 3y) Combine like terms: 4 + -21 = -17 18 + 10y = -17 + 3y Solving 18 + 10y = -17 + 3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3y' to each side of the equation. 18 + 10y + -3y = -17 + 3y + -3y Combine like terms: 10y + -3y = 7y 18 + 7y = -17 + 3y + -3y Combine like terms: 3y + -3y = 0 18 + 7y = -17 + 0 18 + 7y = -17 Add '-18' to each side of the equation. 18 + -18 + 7y = -17 + -18 Combine like terms: 18 + -18 = 0 0 + 7y = -17 + -18 7y = -17 + -18 Combine like terms: -17 + -18 = -35 7y = -35 Divide each side by '7'. y = -5 Simplifying y = -5

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