Đáp án: $S = \left( { - \infty ;\dfrac{{ - 3}}{2}} \right]U\left[ {5; + \infty } \right)$
$\begin{array}{l}
2{x^2} - 7x - 15 \ge 0\\
\Leftrightarrow (2x + 3)(x - 5) \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
2x + 3 \ge 0\\
x - 5 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
2x + 3 \le 0\\
x - 5 \le 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x \ge \dfrac{{ - 3}}{2}\\
x \ge 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x \le \dfrac{{ - 3}}{2}\\
x \le 5
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 5\\
x \le \dfrac{{ - 3}}{2}
\end{array} \right.
\end{array}$
