-log_{0.5}3\\ log_{0.5}(3-2x)>log_{0.5}\frac{1}{3}\\ \\ 3-2x<\frac{1}{3}\\ 3-2x>0 \\ \\ x>\frac{4}{3}\\ x<\frac{3}{2}\\ \\ (\frac{4}{3}; \frac{3}{2})" alt="log_{0.5}(3-2x)>-log_{0.5}3\\ log_{0.5}(3-2x)>log_{0.5}\frac{1}{3}\\ \\ 3-2x<\frac{1}{3}\\ 3-2x>0 \\ \\ x>\frac{4}{3}\\ x<\frac{3}{2}\\ \\ (\frac{4}{3}; \frac{3}{2})" align="absmiddle" class="latex-formula">