Question 294858: x(|x-2|)>=0. x-2 is an absolute value.
I thought the answer was x= all real numbers, but the x on the outside of the bracket messes that up. How do I approach this?
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Absolute value problems are really two problems in one.
Positive solution (where ):

This is true when and also when 
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Negative solution (where ):


Break up the region into three regions,



and test a point to check the inequality
, 


No, not in the valid region.
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, 


Yes, in the valid region.
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, 


No, not in the valid region.
So from the negative solution, the valid region would be (0,2).
Put together with and , then the valid region is,
( )
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