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: 67

Answer

$[\frac{-1}{2},\frac{3}{2})$

Work Step by Step

$\frac{-1}{2} \leq \frac{4x-1}{6} \lt \frac{5}{6}$ Using the inequality properties, multiply all parts by the LCD 6. $6(\frac{-1}{2}) \leq 6(\frac{4x-1}{6}) \lt 6(\frac{5}{6})$ $-3 \leq 4x-1 \lt 5$ Add 1 to all parts. $-3+1 \leq 4x-1+1 \lt 5+1 $ $-2 \leq 4x \lt 6 $ Divide by 4 to get $x$. $\frac{-2}{4} \leq \frac{4x}{4} \lt \frac{6}{4}$ $\frac{-1}{2} \leq x \lt \frac{3}{2}$ In Interval Notation:$[\frac{-1}{2},\frac{3}{2})$
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