5.
0.5\\\log_9(4-3x)>\log_99^{0.5}\\\log_9(4-3x)>\log_93\\4-3x>3>0\\3x<4-3\\3x<1\\\boxed{x<\dfrac13}" alt="\log_9(4-3x)>0.5\\\log_9(4-3x)>\log_99^{0.5}\\\log_9(4-3x)>\log_93\\4-3x>3>0\\3x<4-3\\3x<1\\\boxed{x<\dfrac13}" align="absmiddle" class="latex-formula">
0\end{cases}\\\begin{cases}0<(4-x)(x-1)\leqslant2\\ x>1\end{cases}\\\begin{cases}-x^2+5x-4\leqslant2\\ 11\end{cases}\\\begin{cases}x^2-5x+6\geqslant0\\ 11\end{cases} \\\begin{cases}x\in(-\infty,2]\cup[3,+\infty)\\ 11\end{cases} \\\boxed{x\in(1,2]\cup[3,4)}" alt="\log_{0.5}(4-x)\geqslant\log_{0.5}2-\log_{0.5}(x-1)\\\log_{0.5}(4-x)+\log_{0.5}(x-1)\geqslant\log_{0.5}2\\\begin{cases}\log_{0.5}(4-x)(x-1)\geqslant\log_{0.5}2\\ x-1>0\end{cases}\\\begin{cases}0<(4-x)(x-1)\leqslant2\\ x>1\end{cases}\\\begin{cases}-x^2+5x-4\leqslant2\\ 11\end{cases}\\\begin{cases}x^2-5x+6\geqslant0\\ 11\end{cases} \\\begin{cases}x\in(-\infty,2]\cup[3,+\infty)\\ 11\end{cases} \\\boxed{x\in(1,2]\cup[3,4)}" align="absmiddle" class="latex-formula">
6.
