Solve (x+1)(x-5)>0

$$( x + 1 ) ( x - 5 ) > 0$$

Solve for x

$$x\in \left(-\infty,-1\right)\cup \left(5,\infty\right)$$

Solution Steps

For the product to be positive, x+1 and x-5 have to be both negative or both positive. Consider the case when x+1 and x-5 are both negative.

$$x+1<0 x-5<0$$

The solution satisfying both inequalities is x<-1.

$$x<-1$$

Consider the case when x+1 and x-5 are both positive.

$$x-5>0 x+1>0$$

The solution satisfying both inequalities is x>5.

$$x>5$$

The final solution is the union of the obtained solutions.

$$x<-1\text{; }x>5$$