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2012 AMC 10A Problem 3

Problem 3 of 25EasierAlgebra

A bug crawls along a number line, starting at −2.-2. It crawls to −6,-6, then turns around and crawls to 5.5. How many units does the bug crawl altogether?

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Solution

It crawls a distance of ∣−2−(−6)∣=∣4∣=4 |-2 - (-6)| = |4| = 4 when it moves from −2-2 to −6.-6. It then travels a distance of ∣−6−5∣=∣−11∣=11 |-6 - 5| = |-11| = 11 as it moves from −6-6 to 5.5. The total distance is then 4+11=15. 4 + 11 = 15. Thus, E is the correct answer.

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Concepts: absolute value

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.