9.105. Find the integers $x$, satisfying the inequality $\left|\frac{2}{x-13}\right|>\frac{8}{9}$.
Solution.

From the condition, we have $|x-13|<\frac{9}{4}, x \neq 13$, from which $-\frac{9}{4}<x-3<\frac{9}{4}, \frac{43}{4}<x<\frac{61}{4}$, $x \neq 13 ; x \in\left(\frac{43}{4} ; 13\right) \cup\left(13 ; \frac{61}{4}\right)$. The integer solutions from the union of these intervals will be $x_{1}=11 ; x_{2}=12 ; x_{3}=14 ; x_{4}=15$.

Answer: $x_{1}=11 ; x_{2}=12 ; x_{3}=14 ; x_{4}=15$.