Решите неравенство: x(x+5)-76>5(x-8).

Ответ:

\[\text{\ \ }x(x + 5) - 76 > 5 \cdot (x - 8)\]

\[x^{2} + 5x - 76 > 5x - 40\]

\[x^{2} - 36 > 0\]

\[x^{2} - 36 = 0\]

\[x^{2} = 36\]

\[x = \pm 6\]

\[Ответ:x \in ( - \infty; - 6) \cup (6; + \infty).\]

\[\ (x - 6)(x + 9) > 0\]

\[(x - 6)(x + 9) = 0\]

\[x - 6 = 0\ \ \ \ \ \ \ \ x + 9 = 0\]

\[x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 9\]

\[Ответ:x \in ( - \infty; - 9) \cup (6; + \infty).\]