Решите неравенство: log0,5 (3x-1)-log0,5 (x-1)<log0,5 (x+18)-log0,5 (x+2)

$log_{0.5}(3x-1)-log_{0.5}(x-1)\ \textless \ log_{0.5}(x+18)-log_{0.5}(x+2)$

ОДЗ:
$\left \{ {{3x-1\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \atop {x+18\ \textgreater \ 0\atop{x+2\ \textgreater \ 0} \right.$

$\left \{ {{x\ \textgreater \ \frac{1}{3} } \atop {x\ \textgreater \ 1}} \atop {x\ \textgreater \ -18\atop{x\ \textgreater \ -2} \right.$
$x$ ∈ $(1;+$ ∞ $)$

$log_{0.5}(3x-1)+log_{0.5}(x+2)\ \textless \ log_{0.5}(x+18)+log_{0.5}(x-1)$