9.214. $\left\{\begin{array}{l}\left|x^{2}-4 x\right|<5 \\ |x+1|<3\end{array}\right.$

Solve the system of inequalities:

9.214. $\left\{\begin{array}{l}\left|x^{2}-4 x\right|<5 \\ |x+1|<3\end{array}\right.$
## Solution.

The system of inequalities is equivalent to the system of inequalities

$$
\left\{\begin{array} { l } 
{ x ^ { 2 } - 4 x  - 5 , } \\
{ - 3  0 } \\
{ - 4 < x < 2 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
-1<x<5 \\
x \in R, \\
-4<x<2
\end{array} \Leftrightarrow-1<x<2\right.\right.\right.
$$

Answer: $x \in(-1 ; 2)$.