1. ## Triangle Inequality

|x - y|<=|x|+|y|

Does anyone know if the above is a true statment? Or is it just a lecture typo intending to be either:

|x + y|<=|x|+|y|
|x - y|<=|x|-|y|

2. Is this true $|-y|=|y|~?$

Is this true $\left| {x - y} \right| = \left| {x + \left( { - y} \right)} \right| \leqslant \left| x \right| + \left| { - y} \right|~?$

Thanks