Question

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

O {xx>-4 and x <2}
O {x| X <-4 or x > 2)
O {x} x <-2 or x > 4)
O {X/ x>-2 or x <4}

Answer 1

The solution set to the inequality 5(x - 2)(x + 4) > 0 is x > 2 and x < -4.

Step-by-step explanation:

The solution set to the inequality 5(x - 2)(x + 4) > 0 can be found by considering the signs of the factors $(x - 2)$ and $(x + 4)$. To find the solution set, we need to determine when the inequality is greater than zero.

1. If both factors are positive, then the inequality is satisfied. So we have the solution set: x > 2 and x > -4.
2. If both factors are negative, then the inequality is also satisfied. So we have the solution set: x < 2 and x < -4.
3. If one factor is positive and the other is negative, then the inequality is not satisfied. So there are no solutions in this case.

Combining the above conditions, we can express the solution set as: x > 2 and x < -4.