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

2016 AMC 12B Problem 3 — Solution

2016 AMC 12B Problem 3

Below is the professionally curated solution for Problem 3 of the 2016 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 12B solutions, or check the answer key.

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Concepts:absolute value order of operations

Difficulty rating: 1130

Let $x=-2016.$ What is the value of

$\Big|\;\big|\,|x|-x\,\big|-|x|\;\Big|-x?$

$-2016$

$0$

$2016$

$4032$

$6048$

Solution:

Since $x=-2016,$ $|x|=2016.$ The innermost expression is $|x|-x=2016+2016=4032.$ Then $\big|4032\big|-|x|=4032-2016=2016,$ and the outer absolute value leaves $2016.$ Finally subtracting $x$ gives $2016-(-2016)=4032.$

Thus, the correct answer is D.

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