Question

$$\left. \begin{array} { l } { \frac { x + y + x + y + z + 1 } { z + z } \lt x - 5 } \\ { \text { c h n e n p a n s b e l e s t f o r a n d e d a d s t \right.$$

Solve for x

$\left\{\begin{matrix}x>-\frac{2y+11z+1}{2\left(1-z\right)}\text{, }&z<0\text{ or }z>1\\x\in \mathrm{R}\text{, }&z=1\text{ and }y<-6\\x<-\frac{2y+11z+1}{2\left(1-z\right)}\text{, }&z>0\text{ and }z<1\end{matrix}\right.$

Solve for z

$\left\{\begin{matrix}z>0\text{, }&\left(y<-6\text{ and }x=\frac{11}{2}\right)\text{ or }\left(x>\frac{11}{2}\text{ and }x<-\left(y+\frac{1}{2}\right)\right)\\z<-\frac{2x+2y+1}{11-2x}\text{, }&x>\frac{11}{2}\text{ and }x<-\left(y+\frac{1}{2}\right)\\z\neq 0\text{, }&x=-\left(y+\frac{1}{2}\right)\text{ and }y<-6\\z<0\text{, }&\left(y>-6\text{ and }x=\frac{11}{2}\right)\text{ or }\left(x>-\left(y+\frac{1}{2}\right)\text{ and }x>\frac{11}{2}\right)\\z>-\frac{2x+2y+1}{11-2x}\text{, }&x>\frac{11}{2}\text{ and }x>-\left(y+\frac{1}{2}\right)\\z\in \left(-\frac{2x+2y+1}{11-2x},0\right)\text{, }&x>-\left(y+\frac{1}{2}\right)\text{ and }x<\frac{11}{2}\\z\in \left(0,-\frac{2x+2y+1}{11-2x}\right)\text{, }&x<\frac{11}{2}\text{ and }x<-\left(y+\frac{1}{2}\right)\end{matrix}\right.$