\[1 \leq \frac{2 + 3x}{2} \leq 1,5\]
\[2 \leq 2 + 3x \leq 3\]
\[0 \leq 3x \leq 1\]
\[0 \leq x \leq \frac{1}{3}\]
\[Ответ:\ x \in \left\lbrack 0;\frac{1}{3} \right\rbrack.\]