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

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

Solve for x

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

Solution Steps

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

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

The solution satisfying both inequalities is x<-7.

$$x<-7$$

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

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

The solution satisfying both inequalities is x>2.

$$x>2$$

The final solution is the union of the obtained solutions.

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