Решите неравенство по 1 цифрой

Решите задачу:

$|x-2| \ \textless \ -2x \Rightarrow \left \{ {{x-2\ \textless \ -2x} \atop {x-2\ \textgreater \ 2x}} \right. \\ \left \{ {{x+2x\ \textless \ 2} \atop {x-2x\ \textgreater \ 2}} \right. \left \{ {{3x\ \textless \ 2} \atop {-x\ \textgreater \ 2}} \right. \left \{ {{x\ \textless \ \frac{2}{3} } \atop {x\ \textless \ -2}} \right. \\ x \in (-\infty;-2)$