Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 9: 17


$[-\frac{7}{4}, \frac{9}{4}]$

Work Step by Step

1. In order for the equation to be true, the equation between the absolute value brackets must be between -8 and 8. Redefine the equation to get rid of the absolute value brackets: $|4x-1| \leq 8$ $-8 \leq 4x-1 \leq 8$ 2. Solve each side of the equation $-8 \leq 4x-1$ $-7 \leq 4x$ (Add 1 to each side) $-\frac{7}{4} \leq x$ (Divide each side by 4) $4x-1 \leq 8$ $4x \leq 9$ (Add 1 to each side) $x \leq \frac{9}{4}$ (Divide each side by 4) 3. Since the original equation is said to be less than or equal ($\leq$) to 8, place your final answer in square brackets $[-\frac{7}{4}, \frac{9}{4}]$
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