9.043. $\sqrt{x^{2}-x-12}<x$.
## Solution.

The given inequality is equivalent to the system of inequalities

$$
\left\{\begin{array} { l } 
{ x ^ { 2 } - x - 12 \geq 0 , } \\
{ x > 0 , } \\
{ x ^ { 2 } - x - 12 > 0 } \\
{ x > -12 }
\end{array}\right.} \\
\text { is }
\end{array}\right.\right.
$$

Using the number line, we get $x \in [4 ; \infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-533.jpg?height=136&width=642&top_left_y=160&top_left_x=447)

Answer: $\quad x \in [4 ; \infty)$.