Example 6. Solve the inequality

$$
3|x-1|+x^{2}>7
$$
Solution. The given inequality can be rewritten as

$$
3|x-1|>7-x^{2}
$$

and, consequently, it is equivalent to the system of inequalities

$$
\left[\begin{array}{l}
3 ( x - 1 ) > 7 - x ^ { 2 } , \\
3 ( x - 1 ) < - ( 7 - x ^ { 2 } )
\end{array}\right.
$$

Since $x^{2}+3 x-10=(x+5)(x-2)$, and $x^{2}-3 x-4=(x+1)(x-4)$, the solution set of the system (6), and therefore of the original inequality, consists of the union of two intervals: $(-\infty ;-1) \cup(2 ;+\infty)$.