Solve |x-2y|+|4y-5z|+|z-3x|=2011

$$| x - 2 y | + | 4 y - 5 z | + | z - 3 x | = 2011$$

Solve for x

$$\left\{\begin{matrix}x=y-2z-\frac{2011}{2}\text{, }&y\leq -2z-\frac{2011}{2}\text{ and }y\leq \frac{7z}{3}+\frac{2011}{2}\text{ and }y\geq \frac{5z}{4}\\x=\frac{3z}{2}-\frac{y}{2}+\frac{2011}{4}\text{, }&y\leq \frac{3z}{5}+\frac{2011}{10}\text{ and }y\leq \frac{7z}{3}+\frac{2011}{2}\text{ and }y\geq \frac{5z}{4}\\x=-3y+3z-\frac{2011}{2}\text{, }&y\leq \frac{3z}{5}-\frac{2011}{10}\text{ and }y\geq \frac{8z}{9}-\frac{2011}{6}\text{ and }y\leq \frac{5z}{4}\\x=\frac{3y}{2}-z+\frac{2011}{4}\text{, }&y\leq \frac{2011}{2}-2z\text{ and }y\geq \frac{8z}{9}-\frac{2011}{6}\text{ and }y\leq \frac{5z}{4}\\x=\frac{3y}{2}-z-\frac{2011}{4}\text{, }&y\geq -2z-\frac{2011}{2}\text{ and }y\leq \frac{8z}{9}+\frac{2011}{6}\text{ and }y\geq \frac{5z}{4}\\x=\frac{2011}{2}+3z-3y\text{, }&y\geq \frac{3z}{5}+\frac{2011}{10}\text{ and }y\leq \frac{8z}{9}+\frac{2011}{6}\text{ and }y\geq \frac{5z}{4}\\x=\frac{3z}{2}-\frac{y}{2}-\frac{2011}{4}\text{, }&y\geq \frac{3z}{5}-\frac{2011}{10}\text{ and }y\geq \frac{7z}{3}-\frac{2011}{2}\text{ and }y\leq \frac{5z}{4}\\x=y-2z+\frac{2011}{2}\text{, }&y\geq \frac{2011}{2}-2z\text{ and }y\geq \frac{7z}{3}-\frac{2011}{2}\text{ and }y\leq \frac{5z}{4}\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{-|z-3x|+5z-x+2011}{2}\text{, }&\left(x\leq \frac{z}{3}\text{ or }x\geq \frac{6z+2011}{5}\right)\text{ and }\left(x>\frac{z}{3}\text{ or }x\leq -4z-2011\right)\text{ and }x\leq \frac{7z}{8}+\frac{2011}{4}\text{ and }x\geq -\frac{3z}{4}-\frac{2011}{2}\text{ and }\left(x\leq -4z-2011\text{ or }x\geq \frac{6z+2011}{5}\right)\\y=\frac{|z-3x|+x+5z-2011}{6}\text{, }&x\leq 2011-4z\text{ and }x\geq \frac{6z-2011}{5}\text{ and }x\leq \frac{7z}{8}+\frac{2011}{4}\text{ and }x\geq -\frac{3z}{4}-\frac{2011}{2}\\y=\frac{-|z-3x|+x+5z+2011}{6}\text{, }&x\leq \frac{6z+2011}{5}\text{ and }x\geq -4z-2011\text{ and }x\leq -\frac{3z}{4}+\frac{2011}{2}\text{ and }x\geq \frac{7z}{8}-\frac{2011}{4}\\y=\frac{|z-3x|+5z-x-2011}{2}\text{, }&\left(x\leq \frac{z}{3}\text{ or }x\geq 2011-4z\right)\text{ and }\left(x>\frac{z}{3}\text{ or }x\leq \frac{6z-2011}{5}\right)\text{ and }x\leq -\frac{3z}{4}+\frac{2011}{2}\text{ and }x\geq \frac{7z}{8}-\frac{2011}{4}\text{ and }\left(x\leq \frac{6z-2011}{5}\text{ or }x\geq 2011-4z\right)\end{matrix}\right.$$