SOLUTION: 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?

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
.
.
.
Negative solution (where ):

Break up the region into three regions,

and test a point to check the inequality
,

No, not in the valid region.
.
.
.
,

Yes, in the valid region.
.
.
.
,

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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