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