\[\sin x = - \frac{1}{2};\ \ \ \sqrt{x - 1} < 2.\ \]
\[1)\ \sin x = - \frac{1}{2}\]
\[x = ( - 1)^{n + 1} \bullet \frac{\pi}{6} + \pi\text{n.}\]
\[2)\ \sqrt{x - 1} < 2\]
\[0 \leq x - 1 < 4\]
\[1 \leq x < 5.\]
\[Ответ:\ \ \frac{7\pi}{6};\ \frac{11\pi}{6}.\]