Найдите целые решения системы неравенств: (x+2)(x+3)-x(x+1)>=3x+3; 5x-3<2x+1.

\[\left\{ \begin{matrix} (x + 2)(x + 3) - x(x + 1) \geq 3x + 3 \\ 5x - 3 < 2x + 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x^{2} + 2x + 3x + 6 - x^{2} - x - 3x \geq 3 \\ 5x - 2x < 1 + 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x \geq - 3 \\ x < 4\ \ \ \\ \end{matrix} \right.\ \]

\[- 3 \leq x < 4.\]

\[Ответ:\ - 3 \leq x < 4.\]