Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set: 59

Answer

$(0,\frac{14}{3}]$

Work Step by Step

$-6 \lt 3(x-2) \leq 8$ Using the properties of inequalities, divide all parts by 3 $\frac{-6}{3} \lt \frac{3(x-2)}{3} \leq \frac{8}{3}$ $-2 \lt x-2 \leq \frac{8}{3}$ Add 2 to all parts, $-2+2 \lt x-2 +2 \leq \frac{8}{3}+2$ $0 \lt x \leq \frac{8}{3}+2$ Take LCD $0 \lt x \leq \frac{8+6}{3}$ $0 \lt x \leq \frac{14}{3}$ In Interval Notation: $(0,\frac{14}{3}]$
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