Đáp án:
$\begin{array}{l}
3x + 2 \le 14\\
\Rightarrow 3x \le 12\\
\Rightarrow x \le 4\\
\Rightarrow A = \left( { - \infty ;4} \right]\\
B = \left[ {3m + 2; + \infty } \right)\\
A \cap B \ne \emptyset \\
\Rightarrow 3m + 2 \le 4\\
\Rightarrow 3m \le 2\\
\Rightarrow m \le \frac{2}{3}\\
Vậy\,m \le \frac{2}{3}
\end{array}$