\[\begin{array}{l}
3\sin x + m - 1 = 0\\
\Leftrightarrow \sin x = \frac{{1 - m}}{3}\\
\Rightarrow pt\,\,co\,\,nghiem\,\,\, \Leftrightarrow - 1 \le \frac{{1 - m}}{3} \le 1\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{1 - m}}{3} \ge - 1\\
\frac{{1 - m}}{3} \le 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
1 - m \ge - 3\\
1 - m \le 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m \le 4\\
m \ge - 2
\end{array} \right. \Leftrightarrow - 2 \le m \le 4.
\end{array}\]
