AMC12 2016 12B, Problem 3

Let $x=-2016$. What is the value of $\bigg|$ $||x|-x|-|x|$ $\bigg|$ $-x$?

Solution: By: dragonfly First of all, lets plug in all of the $x$'s into the equation. $\bigg|$ $||-2016|-(-2016)|-|-2016|$ $\bigg|$ $-(-2016)$ Then we simplify to get $\bigg|$ $|2016+2016|-2016$ $\bigg|$ $+2016$ which simplifies into $\bigg|$ $2016$ $\bigg|$ $+2016$ and finally we get $\fbox{4032}$

Answer: 4032