\[\ x(x + 3) - 6 < 3 \cdot (x + 1)\]
\[x^{2} + 3x - 6 < 3x + 3\]
\[x^{2} + 3x - 3x - 6 - 3 < 0\]
\[x^{2} - 9 < 0\]
\[x^{2} - 9 = 0\]
\[x^{2} = 9\]
\[x = \pm 3\]
\[Ответ:x \in ( - 3;\ 3).\]
\[\text{\ \ }(x + 8)(x - 3) > 0\]
\[(x + 8)(x - 3) = 0\]
\[x + 8 = 0\ \ \ \ \ \ \ \ x - 3 = 0\]
\[x = - 8\ \ \ \ \ \ \ \ \ \ \ \ x = 3\]
\[Ответ:\ \ \ x \in ( - \infty;\ - 8) \cup (3;\ + \infty).\]