\(\begin{gathered} \left( {6x - 15} \right)\left( {9x - 24} \right) \leqslant 0 \hfill \\ \Leftrightarrow \left[ \begin{gathered} \left\{ \begin{gathered} 6x - 15 \leqslant 0 \hfill \\ 9x - 24 \geqslant 0 \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} 6x - 15 \geqslant 0 \hfill \\ 9x - 24 \leqslant 0 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right. \Leftrightarrow \left[ \begin{gathered} \left\{ \begin{gathered} 6x \leqslant 15 \hfill \\ 9x \geqslant 24 \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} 6x \geqslant 15 \hfill \\ 9x \leqslant 24 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right. \Leftrightarrow \left[ \begin{gathered} \left\{ \begin{gathered} x \leqslant \frac{5}{2} \hfill \\ x \geqslant \frac{8}{3} \hfill \\ \end{gathered} \right. \hfill \\ \left\{ \begin{gathered} x \geqslant \frac{5}{2} \hfill \\ x \leqslant \frac{8}{3} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \right. \Leftrightarrow x \in \left[ {\frac{5}{2};\frac{8}{3}} \right] \hfill \\ \end{gathered} \)
