Solve the inequality $-2 + x \le 2 - 3x < 9 + 4x$.

1. Split the compound inequality into two inequalities and solve the left part.

From
$-2+x \leqslant 2-3x,$
$x+3x \leqslant 2+2$
$4x \leqslant 4$
$x \leqslant 1.$

2. Solve the right part and combine both conditions.

From
$2-3x < 9+4x,$
$-3x-4x < 9-2$
$-7x < 7.$
Dividing by $-7$ reverses the inequality sign:
$x > -1.$
Combining $x \leqslant 1$ and $x>-1$ gives
$-1 < x \leqslant 1.$