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: 19

Answer

Interval Notation: $(-∞,-4)∪(4,∞)$ Graph:

Work Step by Step

$|x| +2 \gt 6$ To isolate the absolute value expression, add $-2$ to both sides of the inequality. $|x| +2 -2 \gt 6-2$ $|x| \gt 4 $ By [$|X| \gt a = X \lt -a $ or $X \gt a$ ] property, $|x| \gt 4 $ is equivalent to $x \lt -4 $ or $ x \gt 4$ Interval Notation: $(-∞,-4)∪(4,∞)$
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