Solve for x
x\in \left(-\frac{1}{4},\frac{5}{2}\right)
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2x-5>0 4x+1<0
For the quotient to be negative, 2x-5 and 4x+1 have to be of the opposite signs. Consider the case when 2x-5 is positive and 4x+1 is negative.
x\in \emptyset
This is false for any x.
4x+1>0 2x-5<0
Consider the case when 4x+1 is positive and 2x-5 is negative.
x\in \left(-\frac{1}{4},\frac{5}{2}\right)
The solution satisfying both inequalities is x\in \left(-\frac{1}{4},\frac{5}{2}\right).
x\in \left(-\frac{1}{4},\frac{5}{2}\right)
The final solution is the union of the obtained solutions.
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