Solve for x
x\in \left(-\frac{3}{2},\frac{7}{5}\right)
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2x+3>0 5x-7<0
For the quotient to be negative, 2x+3 and 5x-7 have to be of the opposite signs. Consider the case when 2x+3 is positive and 5x-7 is negative.
x\in \left(-\frac{3}{2},\frac{7}{5}\right)
The solution satisfying both inequalities is x\in \left(-\frac{3}{2},\frac{7}{5}\right).
5x-7>0 2x+3<0
Consider the case when 5x-7 is positive and 2x+3 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-\frac{3}{2},\frac{7}{5}\right)
The final solution is the union of the obtained solutions.
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