Answer
$-1 \leq x \lt \frac{1}{2}$
The solution set is $~~[-1, \frac{1}{2})$

Work Step by Step
$4x \lt 2x+1 \leq 3x+2$
$4x \lt 2x+1~~$ and $~~2x+1 \leq 3x+2$
Then:
$4x \lt 2x+1$
$2x \lt 1$
$x \lt \frac{1}{2}$
and
$2x+1 \leq 3x+2$
$-1 \leq x$
Solution:
$-1 \leq x \lt \frac{1}{2}$
The solution set is $~~[-1, \frac{1}{2})$
