$\begin{align}  & -6\le 4-2x<5-x \\ & -6-4\le -2x<5-x-4 \\ & -10\le -2x<1-x \\ & -10\le -2x\text{      }\left| -2x<1-x \right. \\ & 5\ge x\text{              }\left| -x<1 \right. \\ & x\le 5\text{              }\left| x>-1 \right. \\ & -1<x\le 5 \\\end{align}$