Для каждого значения a решите систему неравенств: x^2+7x+6<=0; x<a.

Ответ:

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

\[x^{2} + 7x + 6 = 0\]

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

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

\[(x + 6)(x + 1) \leq 0\]

\[- 6 \leq x \leq - 1.\]

\[Если\ a \leq - 6:\ \]

\[x \in \varnothing.\ \]

\[Если\ - 6 < a \leq - 1:\]

\[- 6 \leq x < a.\ \]

\[Если\ \ a > - 1:\ \]

\[x \in \lbrack - 6;\ - 1\rbrack.\]