Solve for x
x\in \left(2,3\right)
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4x-8<0 6-2x<0
For the product to be positive, 4x-8 and 6-2x have to be both negative or both positive. Consider the case when 4x-8 and 6-2x are both negative.
x\in \emptyset
This is false for any x.
6-2x>0 4x-8>0
Consider the case when 4x-8 and 6-2x are both positive.
x\in \left(2,3\right)
The solution satisfying both inequalities is x\in \left(2,3\right).
x\in \left(2,3\right)
The final solution is the union of the obtained solutions.
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