2016 AMC 10B Problems/Problem 3

Problem

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

$\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048$

Solution

$|-2016|-(-2016) \implies 2016+2016 \implies 4032$ . $4032-|-2016| \implies 4032-2016 \implies 2016$ . $|2016|=2016$ . $2016-(-2016) \implies 2016+2016=\boxed{4032}$ .

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2016 AMC 10B Problems/Problem 3

Problem

Solution