9.2 Find all real numbers $x$ that satisfy the inequality
$$\sqrt{3-x}-\sqrt{x+1}>\frac{1}{2}$$
[Solution] From $3-x \geqslant 0, x+1 \geqslant 0, \sqrt{3-x}>\sqrt{x+1}$, we know
$$-1 \leqslant x<1+\frac{\sqrt{31}}{8}$$.
From (1) and (2), the solution to the original inequality is
$$-1 \leqslant x<1-\frac{\sqrt{31}}{8}$$