Решите неравенство: x(x-7)-18>7(9-x).

Ответ:

\[\ x(x - 7) - 18 > 7 \cdot (9 - x)\]

\[x^{2} - 7x - 18 > 63 - 7x\]

\[x^{2} - 81 > 0\]

\[x^{2} - 81 = 0\]

\[x^{2} = 81\]

\[x = \pm 9\]

\[Ответ:\ x \in ( - \infty; - 9) \cup (9; + \infty).\]

\[\ (x + 9)(x - 3) < 0\]

\[(x + 9)(x - 3) = 0\]

\[x + 9 = 0\ \ \ \ \ \ \ x - 3 = 0\]

\[x = - 9\ \ \ \ \ \ \ \ \ \ \ x = 3\]

\[Ответ:\ x \in ( - 9;3)\text{.\ }\]