\[\boxed{\text{476\ (476).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} 2 \cdot (x - 3) \geq - 3 \cdot (x + 2) \\ \frac{7x}{3} \leq 1 - \frac{x}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \cdot 6\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\text{\ \ \ }\left\{ \begin{matrix} 2x - 6 \geq - 3x - 6 \\ \frac{14x + 3x}{6} \leq 1\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 5x \geq 0\ \ \\ \frac{17x}{6} \leq 1 \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 0 \\ x \leq \frac{6}{17} \\ \end{matrix} \right.\ \]
\[Ответ:x \in \left\lbrack 0;\frac{6}{17} \right\rbrack.\]