Solve the inequality

$-3 \leq 4-\frac{7 x}{2} \leq 18$

$\Rightarrow-3-4 \leq-\frac{7 x}{2} \leq 18-4$

$\Rightarrow-7 \leq-\frac{7 x}{2} \leq 14$

$\Rightarrow 7 \geq \frac{7 x}{2} \geq-14$

$\Rightarrow 1 \geq \frac{x}{2} \geq-2$

$\Rightarrow 2 \geq x \geq-4$

Thus, the solution set for the given inequalityis $[-4,2]$.