Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.7 - Absolute Value Inequalities - Exercise Set: 82

Answer

$(\frac{-3}{4},\frac{17}{4})$

Work Step by Step

$|\frac{4x-7}{5}| \lt 2$ By the property, $|X| \lt a $ is equivalent to $-a \lt X \lt a$, the absolute value expression becomes, $-2 \lt \frac{4x-7}{5} \lt 2$ $-10 \lt 4x-7 \lt 10$ $-10+7 \lt 4x-7+7 \lt 10+7$ $-3 \lt 4x\lt 17$ $\frac{-3}{4} \lt x \lt \frac{17}{4}$ Interval Notation : $(\frac{-3}{4},\frac{17}{4})$
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