24. Find all real numbers $x$ that satisfy the inequality $\sqrt{3-x}-\sqrt{x+1}>\frac{1}{2}$.
24. The arithmetic values of radicals are meant.

From the system of inequalities $\left\{\begin{array}{l}3-x \geqslant 0 \\ x+1 \geqslant 0\end{array}\right.$ it follows that $-1 \leqslant x \leqslant 3$.

The inequality is satisfied for $x < 1+\frac{\sqrt{31}}{8}$.

Considering condition (3), we finally obtain $-1 \leqslant x \leqslant 1-\frac{\sqrt{31}}{8}$.