Solve for x
x\in \left(-\frac{3}{2},-1\right)
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2x+3>0 2x+2<0
For the quotient to be negative, 2x+3 and 2x+2 have to be of the opposite signs. Consider the case when 2x+3 is positive and 2x+2 is negative.
x\in \left(-\frac{3}{2},-1\right)
The solution satisfying both inequalities is x\in \left(-\frac{3}{2},-1\right).
2x+2>0 2x+3<0
Consider the case when 2x+2 is positive and 2x+3 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-\frac{3}{2},-1\right)
The final solution is the union of the obtained solutions.
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