Question

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

Answer 1

Answer:

Step-by-step explanation:

The Answer is {x| x <-4 or x> 2}

Answer 2

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