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

Answer:You selected the correct answer: {x | x < -4 or x > 2}Step-by-step explanation:5(x - 2)(x + 4) > 0Use FOIL method to expand (x - 2)(x + 4): [tex]5(x^{2} + 2x - 8)[/tex] > 0Distribute 5 into [tex](x^{2} + 2x - 8)[/tex][tex]5x^{2} + 10x - 40[/tex] > 0Divide 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 > -2Therefore, the solution set to the inequality is {x | x < -4 or x > 2}Interval notation:  (-∞, -4) ∪ (2, ∞)