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

2016 AMC 10B Problem 3

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Let

x=-2016.

What is the value of

\Bigg\vert\Big\vert |x|-x\Big\vert-|x|\Bigg\vert-x?

\ -2016

\ 0

\ 2016

\ 4032

\ 6048

For

x<0

|x|=-x

Evaluate the absolute values from the inside outward

Since

x=-2016<0,

we have

|x|=2016.

Thus

\begin{aligned} |x|-x&=2016-(-2016) \\ &=4032, \end{aligned}

so the innermost absolute value is

4032.

Therefore the full expression is

|4032-2016|+2016=4032.

Thus, the correct answer is D .