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