Solve for x
x\in \left(-\infty,\frac{3}{4}\right)\cup \left(\frac{5}{2},\infty\right)
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3-4x>0 2x-5<0
For the quotient to be negative, 3-4x and 2x-5 have to be of the opposite signs. Consider the case when 3-4x is positive and 2x-5 is negative.
x<\frac{3}{4}
The solution satisfying both inequalities is x<\frac{3}{4}.
2x-5>0 3-4x<0
Consider the case when 2x-5 is positive and 3-4x is negative.
x>\frac{5}{2}
The solution satisfying both inequalities is x>\frac{5}{2}.
x<\frac{3}{4}\text{; }x>\frac{5}{2}
The final solution is the union of the obtained solutions.
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