При каждом значении параметра a решите неравенство ax+5a<4-6x.

\[ax + 5a < 4 - 6x\]

\[ax + 6x < 4 - 5a\]

\[(a + 6)x < 4 - 5a\]

\[1)\ a = - 6:\]

\[0 \cdot x < 34 \Longrightarrow x - любое \Longrightarrow\]

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

\[2)\ a > - 6:\]

\[x < \frac{4 - 5a}{a + 6} \Longrightarrow\]

\[\Longrightarrow x \in \left( - \infty;\frac{4 - 5a}{a + 6} \right).\]

\[3)\ a < - 6:\]

\[x > \frac{4 - 5a}{a + 6} \Longrightarrow\]

\[\Longrightarrow x \in \left( \frac{4 - 5a}{a + 6}; + \infty \right).\]

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

\[для\ a = - 6;\ \ \]

\[любое\ x \in \left( - \infty;\frac{4 - 5a}{a + 6} \right)\ \]

\[для\ a > - 6;\]

\[любое\ x \in \left( \frac{4 - 5a}{a + 6}; + \infty \right)\text{\ \ }\]

\[для\ a < - 6.\]