Answer
$(-1.5,1.5)$
Work Step by Step
$1 \lt 4+2x \lt 7$
To solve compound inequality,
Add -4 to all three parts.
$1-4 \lt 4+2x-4 \lt 7-4$
$-3 \lt 2x \lt 3$
Divide all parts by 2 to get $x$ alone.
$\frac{-3}{2} \lt \frac{2x}{2} \lt \frac{3}{2}$
$\frac{-3}{2} \lt x \lt \frac{3}{2}$
$-1.5 \lt x \lt 1.5$
In interval notation: $(-1.5,1.5)$
