Решите систему неравенств: 2x-6<=0; x^2+7x+6>0.

Ответ:

\[\left\{ \begin{matrix} 2x - 6 \leq 0\ \ \ \ \ \ \ \ \ \\ x^{2} + 7x + 6 > 0 \\ \end{matrix} \right.\ \]

\[x^{2} + 7x + 6 = (x + 6)(x + 1)\]

\[x_{1} + x_{2} = - 7;\ \ x_{1} \cdot x_{2} = 6\]

\[x_{1} = - 6;\ \ x_{2} = - 1.\]

\[\left\{ \begin{matrix} 2x \leq 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x + 6)(x + 1) > 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x \leq 3\ \ \ \\ x < - 6 \\ x > - 1 \\ \end{matrix} \right.\ \]

\[x < - 6;\]

\[- 1 < x \leq 3.\]

\[Ответ:x < - 6;\ - 1 < x \leq 3.\]