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: 70

Answer

The solution is $(8,9)$

Work Step by Step

$-\dfrac{1}{4}\gt\dfrac{6-x}{12}\gt-\dfrac{1}{6}$ Multiply the whole inequality by $12$: $12\Big(-\dfrac{1}{4}\gt\dfrac{6-x}{12}\gt-\dfrac{1}{6}\Big)$ $-\dfrac{12}{4}\gt6-x\gt-\dfrac{12}{6}$ $-3\gt6-x\gt-2$ Subtract $6$ from each side: $-3-6\gt6-6-x\gt-2-6$ $-9\gt-x\gt-8$ Change the sign of all three sides: $9\gt x\gt8$ Expressing the solution in interval notation: $(8,9)$
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