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: 23

Answer

Interval Notation: $(-∞,\frac{2}{3})∪(2,∞)$ Graph

Work Step by Step

$|6x-8|+3 \gt 7$ By adding $-3$ to both sides of the inequality, isolate the absolute value expression. $|6x-8|+3- 3 \gt 7-3$ $|6x-8| \gt 4$ Using absolute value inequality property, $6x - 8 \lt -4$ or $6x-8 \gt 4$ Add $8$ to both sides of the inequalities, $6x - 8+8 \lt -4+8 $ or $6x-8 +8 \gt 4+8$ $6x \lt 4$ or $6x \gt 12$ Divide by $6$ to both sides of the inequalities, $x \lt \frac{4}{6}$ or $x \gt \frac{12}{6}$ $x \lt \frac{2}{3}$ or $x \gt 2$ Interval Notation: $(-∞,\frac{2}{3})∪(2,∞)$
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