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: 45



Work Step by Step

We are asked to solve the absolute value inequality: $|2x-6|\lt 8$ We remove the absolute value sign by splitting the inequality into two as follows: $-8 \lt 2x-6 \lt 8$ Now, we solve for (isolate) $x$: $-8+6 \lt 2x-6+6 \lt 8+6$ $-2\div 2 \lt 2x\div 2 \lt 14\div 2$ $-1 \lt x \lt 7$ In interval notation, this can be written as: $(-1,7)$ See the number line graph below.
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