Solve for x
x\in \left(11,17\right)
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x-11<0 17-x<0
For the product to be positive, x-11 and 17-x have to be both negative or both positive. Consider the case when x-11 and 17-x are both negative.
x\in \emptyset
This is false for any x.
17-x>0 x-11>0
Consider the case when x-11 and 17-x are both positive.
x\in \left(11,17\right)
The solution satisfying both inequalities is x\in \left(11,17\right).
x\in \left(11,17\right)
The final solution is the union of the obtained solutions.
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