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