\[\boxed{\mathbf{59}.}\]
\[\left\{ \begin{matrix} \frac{x - 2}{5} \geq \frac{x - 3}{6}\ \ \ | \cdot 30 \\ 5x - 1 < 3 \cdot (x + 1)\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} 6x - 12 \geq 5x - 15 \\ 5x - 1 < 3x + 3\ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x \geq - 3 \\ 2x < 4\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq - 3 \\ x < 2\ \ \ \ \\ \end{matrix} \right.\ \]
\[- 3 \leq x < 2\]
\[Целые\ решения:\]
\[- 3;\ - 2;\ - 1;0;1.\]