Solve (x+5)(x-9)>0

$$( x + 5 ) ( x - 9 ) > 0$$

Solve for x

$$x\in \left(-\infty,-5\right)\cup \left(9,\infty\right)$$

Solution Steps

For the product to be positive, x+5 and x-9 have to be both negative or both positive. Consider the case when x+5 and x-9 are both negative.

$$x+5<0 x-9<0$$

The solution satisfying both inequalities is x<-5.

$$x<-5$$

Consider the case when x+5 and x-9 are both positive.

$$x-9>0 x+5>0$$

The solution satisfying both inequalities is x>9.

$$x>9$$

The final solution is the union of the obtained solutions.

$$x<-5\text{; }x>9$$