Problem #WSP-100009

Problem

For any real number $x$, the absolute value of $x$, written $\left|x\right|$, is defined to be $x$ if $x>0$ and $-x$ if $x\le 0$. What are $\left|3\right|$, $|-4.3|$ and $\left|0\right|$?

Let $x$ and $y$ be real numbers. Prove that $x\le \left|x\right|$ and $0\le \left|x\right|$. Then prove that the following inequality holds $|x+y|\le \left|x\right|+\left|y\right|$.