Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 4 - Section 4.3 - Equations and Inequalities Involving Absolute Value - Exercise Set - Page 283: 46

Answer

$(-\frac{22}{3},4)$

Work Step by Step

We are asked to solve the absolute value inequality: $|3x+5|\lt 17$ We remove the absolute value sign by splitting the inequality into two as follows: $-17 \lt 3x+5 \lt 17$ Now, we solve for (isolate) $x$: $-17-5 \lt 3x+5-5 \lt 17-5$ $-22 \lt 3x \lt 12$ $-22\div 3 \lt 3x\div 3 \lt 12\div 3$ $-\frac{22}{3} \lt x \lt 4$ In interval notation, this can be written as: $(-\frac{22}{3},4)$ See the number line graph below.
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