In trying to solve the following inequality in R:
|x+y| |y+z|+|z+x| $\displaystyle \leq$ |x+y+z| |x| +|y| + |z|,i tried a proof by contradiction.
So suppose the above inequality is not true ,then we have:
|x+y| |y+z|+|z+x| > |x+y+z| |x| +|y| + |z|
....................or 2|x| +2|y| +2|z| > |x+y+z| +|x| +|y| +|z|
.....................or |x| +|y| + |z|> |x+y+z| and here is where i get stuck because i cannot derive a contradiction