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