# Solve the following inequality. (x + 2)*(x - 4) >= 0 [Please give the correct answer]

justaguide | Certified Educator

The inequality `(x + 2)*(x - 4) >= 0` has to be solved.

The product of 2 numbers is greater than or equal to 0 only if either both of them are greater than or equal to 0 or both of them are less than or equal to 0.

For the given inequality `(x + 2)*(x - 4) >= 0` if:

• `x +2 >= 0` and `x - 4 >= 0`

=> `x >= -2` and `x >= 4`

x lies in `(4, oo)`

• `x + 2 <= 0` and `x - 4 <= 0`

=> `x <= -2` and `x <= 4`

x lies in `(-oo, -2)`

The solution of the given inequality is `(-oo, -2)U(4, oo)`

embizze | Certified Educator

Solve `(x-2)(x+4)>=0 ` :

There are three intervals to consider:

(1) If x<-4 the product on the left is positive

(2) If -4<x<2 the product on the left is negative

(3) If x>2 the product on the left is positive.

To check each interval try a test value, e.g. x=-5, x=0, and x=3.

Thus the solution is `x<=-4 ` or `x>=2 ` .

In interval notation `(-oo,-4]uu[2,oo) `

The graph of y=(x-2)(x+4):

justaguide | Certified Educator

The inequality is (x + 2)*(x - 4) >= 0 not (x - 2)*(x + 4) >= 0.