Issolvi |x|+|y|>|x+z|

$$| x | + | y | > | x + z |$$

Solvi għal x

$$\left\{\begin{matrix}x<-z\text{, }&(z<0\text{ and }y<z)\text{ or }(y>-z\text{ and }z<0)\\x<-z\text{, }&(z\geq 0\text{ and }y<0)\text{ or }(z\geq 0\text{ and }y>-z\text{ and }y\geq 0)\\x\in [-z,\frac{y-z}{2})\text{, }&y\leq z\text{ and }y>-z\text{ and }y\geq 0\\x\in [-z,0)\text{, }&(z>0\text{ and }y<-z)\text{ or }(z>0\text{ and }y>z)\\x\in [-z,\frac{-y-z}{2})\text{, }&y\geq -z\text{ and }y<0\\x\in (\frac{-y-z}{2},-z)\text{, }&y\leq -z\text{ and }y>z\text{ and }y\geq 0\\x\geq 0\text{, }&(z\geq 0\text{ and }y<-z)\text{ or }(z\geq 0\text{ and }y>z)\\x\geq -z\text{, }&z<0\\x\in (\frac{y-z}{2},-z)\text{, }&y\geq z\text{ and }y<0\end{matrix}\right.$$

Solvi għal z

$$z\in \left(-\left(|x|+|y|+x\right),|x|+|y|-x\right)$$

$$x<0\text{ or }\left(x>-|y|\text{ and }x\geq 0\right)$$