Answer
$3 \lt x \lt 7$
The solution set is $~~(3, 7)$

Work Step by Step
$2x-3 \lt x+4 \lt 3x-2$
$2x-3 \lt x+4~~$ and $~~x+4 \lt 3x-2$
Then:
$2x-3 \lt x+4$
$x \lt 7$
and
$x+4 \lt 3x-2$
$6 \lt 2x$
$3 \lt x$
Solution:
$3 \lt x \lt 7$
The solution set is $~~(3, 7)$
