Solve (x+2)(x-7)>0

$$( x + 2 ) ( x - 7 ) > 0$$

Solve for x

$$x\in \left(-\infty,-2\right)\cup \left(7,\infty\right)$$

Solution Steps

For the product to be positive, x+2 and x-7 have to be both negative or both positive. Consider the case when x+2 and x-7 are both negative.

$$x+2<0 x-7<0$$

The solution satisfying both inequalities is x<-2.

$$x<-2$$

Consider the case when x+2 and x-7 are both positive.

$$x-7>0 x+2>0$$

The solution satisfying both inequalities is x>7.

$$x>7$$

The final solution is the union of the obtained solutions.

$$x<-2\text{; }x>7$$