Answer
$(-2,5)$
Work Step by Step
$|2x-3| \lt 7$
This is equivalent to
$-7 \lt 2x-3 \lt 7$
Using inequality properties, add $3 $ to all three parts.
$-7+3 \lt 2x-3+3 \lt 7+3$
$-4 \lt 2x \lt 10$
Divide all parts by $2 $
$\frac{-4}{2} \lt \frac{2x}{2} \lt \frac{10}{2}$
$-2 \lt x \lt 5$
In Interval Notation: $(-2,5)$