Solve for x
x\in \left(\frac{2}{5},4\right)
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2-5x>0 4-x<0
For the product to be negative, 2-5x and 4-x have to be of the opposite signs. Consider the case when 2-5x is positive and 4-x is negative.
x\in \emptyset
This is false for any x.
4-x>0 2-5x<0
Consider the case when 4-x is positive and 2-5x is negative.
x\in \left(\frac{2}{5},4\right)
The solution satisfying both inequalities is x\in \left(\frac{2}{5},4\right).
x\in \left(\frac{2}{5},4\right)
The final solution is the union of the obtained solutions.
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