Solve for x
x\in \left(1,3\right)
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2-2x>0 3-x<0
For the product to be negative, 2-2x and 3-x have to be of the opposite signs. Consider the case when 2-2x is positive and 3-x is negative.
x\in \emptyset
This is false for any x.
3-x>0 2-2x<0
Consider the case when 3-x is positive and 2-2x is negative.
x\in \left(1,3\right)
The solution satisfying both inequalities is x\in \left(1,3\right).
x\in \left(1,3\right)
The final solution is the union of the obtained solutions.
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