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?

Algebra ->  Absolute-value -> 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?      Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
Absolute value problems are really two problems in one.
Positive solution (where abs%28x-2%29=%28x-2%29):
x%28x-2%29%3E=0
This is true when x%3E=2 and also when x=0
.
.
.
Negative solution (where abs%28x-2%29=-%28x-2%29):
x%2A%28-%28x-2%29%29%3E=0
x%2A%28x-2%29%3C=0
Break up the region into three regions,
+x%3C0+
+0%3Cx%3C2
+x%3E2
and test a point to check the inequality
+x%3C0, +x=-1
+-1%28-1-2%29%3C=0
+3%3C=0
No, not in the valid region.
.
.
.
+0%3Cx%3C2, +x=1
+1%281-2%29%3C=0
+-1%3C=0
Yes, in the valid region.
.
.
.
+x%3E2, +x=3
+3%283-2%29%3C=0
+3%3C=0
No, not in the valid region.
So from the negative solution, the valid region would be (0,2).
Put together with x=0 and x%3E2, then the valid region is,
(x%3E=0)