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: 52

Answer

y=1

Work Step by Step

Simplifying 4y + 7 + -3(2y + 3) = 4(3y + -4) + -7y + 7 Reorder the terms: 4y + 7 + -3(3 + 2y) = 4(3y + -4) + -7y + 7 4y + 7 + (3 * -3 + 2y * -3) = 4(3y + -4) + -7y + 7 4y + 7 + (-9 + -6y) = 4(3y + -4) + -7y + 7 Reorder the terms: 7 + -9 + 4y + -6y = 4(3y + -4) + -7y + 7 Combine like terms: 7 + -9 = -2 -2 + 4y + -6y = 4(3y + -4) + -7y + 7 Combine like terms: 4y + -6y = -2y -2 + -2y = 4(3y + -4) + -7y + 7 Reorder the terms: -2 + -2y = 4(-4 + 3y) + -7y + 7 -2 + -2y = (-4 * 4 + 3y * 4) + -7y + 7 -2 + -2y = (-16 + 12y) + -7y + 7 Reorder the terms: -2 + -2y = -16 + 7 + 12y + -7y Combine like terms: -16 + 7 = -9 -2 + -2y = -9 + 12y + -7y Combine like terms: 12y + -7y = 5y -2 + -2y = -9 + 5y Solving -2 + -2y = -9 + 5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5y' to each side of the equation. -2 + -2y + -5y = -9 + 5y + -5y Combine like terms: -2y + -5y = -7y -2 + -7y = -9 + 5y + -5y Combine like terms: 5y + -5y = 0 -2 + -7y = -9 + 0 -2 + -7y = -9 Add '2' to each side of the equation. -2 + 2 + -7y = -9 + 2 Combine like terms: -2 + 2 = 0 0 + -7y = -9 + 2 -7y = -9 + 2 Combine like terms: -9 + 2 = -7 -7y = -7 Divide each side by '-7'. y = 1 Simplifying y = 1
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