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

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9.174. $|x-3|^{2 x^{2}-7 x}>1$.
## Solution.

Rewrite the inequality as $|x-3|^{2 x^{2}-7 x}>|x-3|^{0}$. It is equivalent to the following conjunction of two systems of inequalities:

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0686.jpg?height=565&width=860&top_left_y=1365&top_left_x=153)

The solution to the first system of inequalities is $(2 ; 3) \cup\left(3 ; \frac{7}{2}\right)$.

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0687.jpg?height=155&width=431&top_left_y=209&top_left_x=382)

The solution to the second system of inequalities is $(-\infty ; 0) \cup(4 ;+\infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0687.jpg?height=156&width=455&top_left_y=451&top_left_x=370)

Answer: $x \in(-\infty ; 0) \cup(2 ; 3) \cup\left(3 ; \frac{7}{2}\right) \cup(4 ; \infty)$.