При каждом значении параметра a решите неравенство ax+7a<2-4x.

\[ax + 7a < 2 - 4x\]

\[ax + 4x < 2 - 7a\]

\[(a + 4)x < 2 - 7a\]

\[1)\ a = - 4:\]

\[0 \cdot x < 30 \Longrightarrow верно\ \]

\[при\ любом\ x \Longrightarrow ( - \infty; + \infty).\]

\[2)\ a > - 4:\]

\[x < \frac{2 - 7a}{a + 4} \Longrightarrow \left( - \infty;\frac{2 - 7a}{a + 4} \right).\]

\[3)\ a < - 4:\]

\[x > \frac{2 - 7a}{a + 4} \Longrightarrow \left( \frac{2 - 7a}{a + 4}; + \infty \right).\]

\[Ответ:\ \ любое\ x \in ( - \infty; + \infty)\ \]

\[для\ a = - 4;\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ любое\ x \in \left( - \infty;\frac{2 - 7a}{a + 4} \right)\text{\ \ }\]

\[для\ a > - 4;\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ любое\ x \in \left( \frac{2 - 7a}{a + 4}; + \infty \right)\text{\ \ }\]

\[для\ a < - 4.\]