Решите неравенство: x(x-5)-29>5(4-x).

Ответ:

\[\text{\ \ }x(x - 5) - 29 > 5 \cdot (4 - x)\]

\[x^{2} - 5x - 29 > 20 - 5x\]

\[x^{2} - 49 > 0\]

\[x^{2} - 49 = 0\]

\[x^{2} = 49\]

\[x = \pm 7\]

\[Ответ:\ \ x \in ( - \infty; - 7) \cup (7;\ + \infty).\]

\[\ (x - 4)(x + 7) < 0\]

\[(x - 4)(x + 7) = 0\]

\[x - 4 = 0\ \ \ \ \ \ x + 7 = 0\]

\[x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 7\ \]

\[Ответ:\ \ x \in ( - 7;4).\]