Помогите решить log0,5(1-3x) больше или равно -2

Решите задачу:

$log_{0.5}(1-3x) \geq -2\\ ===================\\ 1-3x\ \textgreater \ 0\\ -3x\ \textgreater \ -1\\ x\ \textless \ \frac{1}{3} \\ ===================\\ log_{0.5}(1-3x) \geq -2\cdot log_{0.5}0.5\\ log_{0.5}(1-3x) \geq log_{0.5}( \frac{1}{2} )^{-2}\\ log_{0.5}(1-3x) \geq log_{0.5}4\\ 0\ \textless \ 0.5\ \textless \ 1 \Rightarrow \\ 1-3x \leq 4\\ -3x \leq 3\\ x \geq -1\\ ===================\\\\ \left \{ {{x\ \textless \ \frac{1}{3}} \atop {x \geq -1}} \right. \Rightarrow x \in [-1; \frac{1}{3} )$