Question

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

Answer 1

Answer:

You selected the correct answer: {x | x < -4 or x > 2}

Step-by-step explanation:

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

Use FOIL method to expand (x - 2)(x + 4):

$5(x^{2} + 2x - 8)$ > 0

Distribute 5 into $(x^{2} + 2x - 8)$

$5x^{2} + 10x - 40$ > 0

Divide all terms by 5 from both sides of the inequality:

$\frac{5x^{2}}{5} + \frac{10x}{5} - \frac{40}{5} > \frac{0}{5}$

$x^{2} + 2x - 8 > 0$

Factor the trinomial:

(x + 4) ( x - 2)  > 0

x < -4 or x > -2

Therefore, the solution set to the inequality is {x | x < -4 or x > 2}

Interval notation:  (-∞, -4) ∪ (2, ∞)