Prove that $|x+y+z| \le |x|+|y| +| z|$ for all $x, y, z$ 
Prove that $$\lvert x+y+z \rvert \le \lvert x \rvert  + \lvert y \rvert + \lvert z\rvert $$ for all $x, y, z$.


You can prove it by using triangle inequality of two numbers.Consider $(y+z)$ as a single entity,$|x+(y+z)|\le |x|+|y+z| $, now use triangle inequality on $|y+z|$, and you will get your answer.
