Question

Which set of intervals represents the solution to the inequality x^2 + 11x + 28 > 0?

A) (-[infinity], -7) ∪ (-4, [infinity])
B) (-7, -4]
C) (-[infinity], -7) ∩ (-4, [infinity])
D) (7, -4)

What is the solution to the inequality x^2 - x - 13 < 0?

A) {-3}
B) (-[infinity], -3)
C) (-3, 4)
D) [-3, 4]

Answer 1

The solution to the inequality x^2 + 11x + 28 > 0 is (-∞, -7) ∪ (-4, ∞). The solution to the inequality x^2 - x - 13 < 0 is (-∞, -3).

Step-by-step explanation:

The solution to the inequality x^2 + 11x + 28 > 0 can be found by using the factored form of the quadratic equation. The quadratic equation can be factored as (x + 4)(x + 7) > 0. To find the solution, we examine the sign of each factor. The inequality is satisfied when both factors are greater than zero or both factors are less than zero. Therefore, the solution is the interval (-∞, -7) ∪ (-4, ∞), which corresponds to option A.

The solution to the inequality x^2 - x - 13 < 0 can also be found using the factored form of the quadratic equation. The quadratic equation can be factored as (x - 4)(x + 3) < 0. To find the solution, we examine the sign of each factor. The inequality is satisfied when one factor is greater than zero and the other factor is less than zero. Therefore, the solution is the interval (-∞, -3), which corresponds to option B.