$4\frac{5}{9}:2\frac{5}{18}-7<x<(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}):(-21\frac{1}{2})$
$\Leftrightarrow \frac{41}{9}:\frac{41}{18}-7<x<(\frac{16}{5}:\frac{16}{5}+\frac{9}{2}.\frac{76}{45}):\frac{-43}{2}$
$\Leftrightarrow \frac{41}{9}.\frac{18}{41}-7<x<(1+\frac{38}{5}).\frac{-2}{43}$
$\Leftrightarrow 2-7<x<\frac{43}{5}.\frac{-2}{43}$
$-5<x<\frac{-2}{5}$
Mà $x\in Z\Rightarrow x\in ${$-4;-3;-2;-1$}