Answer
The solution set is $[-10,\infty)$.
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
---
$\displaystyle \frac{x}{4}-\frac{3}{2}\leq\frac{x}{2}+1\qquad $ ... $/\times 4$
$ x-6\leq 2x+4\qquad $ ... $/-2x+6$
$-x\leq 10 \qquad $ ... $/\div(-1) \quad $ (negative)
$ x\geq-10$
The solution set is $[-10,\infty)$.
