Solve 3m+39/2m+9>0

$$\frac{ 3m+39 }{ 2m+9 } > 0$$

Solve for m

$$m\in \left(-\infty,-13\right)\cup \left(-\frac{9}{2},\infty\right)$$

Solution Steps

For the quotient to be positive, 3m+39 and 2m+9 have to be both negative or both positive. Consider the case when 3m+39 and 2m+9 are both negative.

$$3m+39<0 2m+9<0$$

The solution satisfying both inequalities is m<-13.

$$m<-13$$

Consider the case when 3m+39 and 2m+9 are both positive.

$$2m+9>0 3m+39>0$$

The solution satisfying both inequalities is m>-\frac{9}{2}.

$$m>-\frac{9}{2}$$

The final solution is the union of the obtained solutions.

$$m<-13\text{; }m>-\frac{9}{2}$$