9.033. $\left|x^{2}-5 x\right|<6$.

Solve the inequality $\left|x^{2}-5 x\right|<6$.
## Solution.

Using the geometric meaning of the modulus, we get that

$$
-6 < x < 6 \quad \text{and} \quad (x+1)(x-6) < 0
$$

This can be written as:

$$
\left\{\begin{array}{l}
(x+1)(x-6) < 0 \\
(x-2)(x-3) > 0
\end{array} \right.
$$

Using the number line, we get \( x \in (-1 ; 2) \cup (3 ; 6) \).

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-529.jpg?height=136&width=644&top_left_y=816&top_left_x=380)

Answer: \( x \in (-1 ; 2) \cup (3 ; 6) \).