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
$$
-1 \leqslant x<1-\frac{\sqrt{31}}{8}.
$$