8.42 Find the integers $x$, satisfying the inequality $\left|\frac{2}{x-13}\right|>\frac{8}{9}$
8.42 Here, the condition $x-13 \neq 0$ must be satisfied, i.e., $x \neq 13$. At the same time, $\left|\frac{2}{x-13}\right|>0$ and this inequality is equivalent to the following: $\left|\frac{x-13}{2}\right|<\frac{9}{8}$. Solving it, we get

$$
-\frac{9}{8}<\frac{x-13}{2}<\frac{9}{8} ;-9<4 x-52<9 ; 43<4 x<61
$$

Thus, $10.75<x<15.25$ and $x \neq 13$. The integer values of $x$ that satisfy these conditions are $11, 12, 14$, 15.

Answer: $11 ; 12 ; 14 ; 15$.