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 - Page 105: 13

Answer

Interval Notation : $[0,12]$ Graph:

Work Step by Step

$|x-6| - 7 \leq -1$ To isolate an absolute value, add $7$ to both sides. $|x-6| - 7 +7 \leq -1+7 $ $|x-6| \leq 6$ By the absolute value inequality property, this is equivalent to $-6 \leq x-6 \leq 6$ Add $6$ to all parts, $-6+6 \leq x-6+6 \leq 6+6$ $0\leq x \leq 12 $ Interval Notation :$[0,12]$
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