Answer:
(-∞, -4) U (2,∞)
Step-by-step explanation:
5(x – 2)(x + 4) > 0
First we solve for x, we replace the inequality sign by = sign
5(x – 2)(x + 4) = 0
Divide both sides by 5
(x – 2)(x + 4) = 0
Now we set each factor =0 and solve for x
x-2 =0 , so x= 2
x+4 =0, so x= -4
Now we use number line and make three intervals
First interval -infinity to -4
second interval -4 to 2
third interval 2 to infinity
Now we check each interval with our inequality
First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5
5(-5 – 2)(-5 + 4) > 0
35>0 is true
second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0
5(0– 2)(0 + 4) > 0
-40>0 is false
Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3
5(3 – 2)(3 + 4) > 0
35>0 is true
solution set are the intervals that make the inequalities true
(-∞, -4) U (2,∞)
