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

Solution:

The given inequality is

5(x - 2)(x + 4) > 0

Divide both sides by 5

(x - 2) (x + 4) > 0

Let us consider

x - 2 = 0 and x + 4 = 0

x = 2 and x = -4

Let us make use of each root to create the test interval

x < -4

- 4 < x < 2

x > 2

Here

x < -4 is true

- 4 < x < 2 is false

x > 2 is true

The solution contains all true intervals

x < -4 or x > 2

i.e. (- ∞, -4) U (2, ∞)

Therefore, the solution set to the inequality is (- ∞, -4) U (2, ∞).

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

Summary:

The solution set to the inequality 5(x - 2)(x + 4) > 0 is (- ∞, -4) U (2, ∞).