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: 60

Answer

x = -0.5

Work Step by Step

Simplifying 5x + -2.5(7 + -4x) = x + -7(4 + x) 5x + (7 * -2.5 + -4x * -2.5) = x + -7(4 + x) 5x + (-17.5 + 10x) = x + -7(4 + x) Reorder the terms: -17.5 + 5x + 10x = x + -7(4 + x) Combine like terms: 5x + 10x = 15x -17.5 + 15x = x + -7(4 + x) -17.5 + 15x = x + (4 * -7 + x * -7) -17.5 + 15x = x + (-28 + -7x) Reorder the terms: -17.5 + 15x = -28 + x + -7x Combine like terms: x + -7x = -6x -17.5 + 15x = -28 + -6x Solving -17.5 + 15x = -28 + -6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6x' to each side of the equation. -17.5 + 15x + 6x = -28 + -6x + 6x Combine like terms: 15x + 6x = 21x -17.5 + 21x = -28 + -6x + 6x Combine like terms: -6x + 6x = 0 -17.5 + 21x = -28 + 0 -17.5 + 21x = -28 Add '17.5' to each side of the equation. -17.5 + 17.5 + 21x = -28 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 21x = -28 + 17.5 21x = -28 + 17.5 Combine like terms: -28 + 17.5 = -10.5 21x = -10.5 Divide each side by '21'. x = -0.5 Simplifying x = -0.5
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