Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2016 AMC 10B Problems/Problem 3"

(Created page with "==Problem== Let <math>x=-2016</math>. What is the value of <math>\bigg|</math> <math>|x|-x|-|x|</math> <math>\bigg|</math> <math>-x</math>? <math>\textbf{(A)}\ -2016\qquad\t...")
 
m (basic solution; someone should add detailed edits in; this was rushed.)
Line 4: Line 4:
  
 
<math>\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048</math>
 
<math>\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048</math>
 +
 +
==Solution==
 +
<math>|-2016|-(-2016) \implies 2016+2016 \implies 4032</math>.
 +
<math>4032-|-2016| \implies 4032-2016 \implies 2016</math>.
 +
<math>|2016|=2016</math>.
 +
<math>2016-(-2016) \implies 2016+2016=\boxed{4032}</math>.

Revision as of 10:56, 21 February 2016

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

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2016_AMC_10B_Problems/Problem_3&oldid=76602"