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

2016 AMC 10B Problem 3 — Solution

2016 AMC 10B Problem 3

Attempt Problem 3 of the 2016 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 10B solutions, or check the answer key.

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Let $x=-2016.$ What is the value of $\Bigg\vert\Big\vert |x|-x\Big\vert-|x|\Bigg\vert-x?$

$\ -2016$

$\ 0$

$\ 2016$

$\ 4032$

$\ 6048$

Answer: D

Concepts:absolute value

Difficulty rating: 960

Solution:

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 .

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