Elementary Algebra

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

Chapter 11 - Additional Topics - 11.1 - Equations and Inequalities Involving Absolute Value - Problem Set 11.1: 34

Answer

{$-\frac{19}{4},\frac{33}{4}$}

Work Step by Step

Using the rules for absolute values to generate two equations, we obtain: Step 1: $|-4x+7|=26$ Step 2: $-4x+7=26$ and $-4x+7=-26$ Step 3: $-4x=26-7$ and $-4x=-26-7$ Step 4: $-4x=19$ and $-4x=-33$ Step 5: $x=\frac{19}{-4}$ and $x=\frac{-33}{-4}$ Step 6: $x=-\frac{19}{4}$ and $x=\frac{33}{4}$ Therefore, the solution set for the equation is {$-\frac{19}{4},\frac{33}{4}$}.
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