Answer:
(-∞,4) U (2,∞)
Step-by-step explanation:
5(x – 2)(x + 4) > 0
to solve this inequality , first we replace > symbol by =
5(x – 2)(x + 4) = 0
solve for x
5(x-2)=0
x-2=0 so x= 2
x+4=0 so x= -4
Now we make a number line
use the x values and break the number line into three intervals
-infinity to -4 , -4 to 2 , 2 to infinity
Pick a number from each interval and check with our inequality
-infinity to -4 , pick -6
5(x – 2)(x + 4) > 0
5(-6 – 2)(-6 + 4) > 0
80>0 , true
So (-∞,4) satisfies our inequality
-4 to 2 , pick 0
5(x – 2)(x + 4) > 0
5(0 – 2)(0+ 4) > 0
-40>0 , False
2 to infinity , pick 3
5(x – 2)(x + 4) > 0
5(3 – 2)(3 + 4) > 0
35>0 , true
So (2,∞) satisfies our inequality
