Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - 3.4 - Equations Involving Parentheses and Fractional Forms - Problem Set 3.4: 94

Answer

a) All reals b) No solution c) 0 d) 0 e) No solution f) All reals g) No solutions h) All reals i) 0

Work Step by Step

We simplify each side of the expression. If the two sides of the equation are the same, the solution is all real numbers. If they are two values that cannot be equal, the answer is no solution. a) $ -2x + 2 = -2x +2 \space \text{all real numbers}$ b) $3x + 4 = 3x -4 \\ 4 = -4 \space \text{no solution}$ c) $ 5x - 5 = -5x -5 \\ 10x =0 \\ x=0$ d) $\frac{x-3}{3} = -1 \\ x-3 = -3 \\ x = 0$ e) $1 = \frac{-2-2}{3} \\ 1 = -4/3 \space \text{no solution}$ f) $ -2 = -10/5 \\ -2 = -2 \space \text{all real numbers}$ g) $4x-8 -2x -6 = 2x +6 \\ -14 =6 \space \text{no solution}$ h) $ 5x+15 -3x +15 = 2x + 30 \\ 30 = 30 \space \text{all real numbers}$ i) $ 7x -7 +4x-8 = 15x -15 \\ 4x =0 \\ x =0 $
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