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):
[tex]5(x^{2} + 2x - 8)[/tex] > 0
Distribute 5 into [tex](x^{2} + 2x - 8)[/tex]
[tex]5x^{2} + 10x - 40[/tex] > 0
Divide all terms by 5 from both sides of the inequality:
[tex]\frac{5x^{2}}{5} + \frac{10x}{5} - \frac{40}{5} > \frac{0}{5}[/tex]
[tex]x^{2} + 2x - 8 > 0[/tex]
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, ∞)
