Triangle inequality with minus

Question

Is the following inequality valid: $$|x-y|\le|x|+|y|$$ I couldn't find this explicitly stated but using the triangle inequality: $$|x+(-y)| \le |x| + |-y| = |x| + |y|.$$ I wanted to clarify that this result was correct.

Answer 1

Yes indeed you are correct (and you've certainly shown) that this follows from the triangle inequality.