How to Solve for Interval with Abs and Max Functions?

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zli034
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Hi all:

The inequality here involves abs, and max functions, how to solve for the interval as show below?
attachment.php?attachmentid=58110&d=1366636107.jpg
 

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The very first thing you should probably do is draw the functions.
This will require you to think already about, for example, when the max switches from one expression to the other, and what the abs does here.
 

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