Question

Consider the following sets.

U = {all real number points on a number line}
A = {solutions to the inequality 3x + 4 ≥ 13}
B = {solutions to the inequality One-halfx + 3 ≤ 4}

For which values of x is A ⋃ B = Ø?

2 < x < 3
2 ≤ x ≤ 3
x ≤ 2 and x ≥ 3
x < 2 and x > 3

Answer 1

Solve each:

3x + 4 ≥ 13 → 3x ≥ 9 → x ≥ 3, so A = [3, ∞).
(1/2)x + 3 ≤ 4 → (1/2)x ≤ 1 → x ≤ 2, so B = (-∞, 2].

A ∪ B = (-∞,2] ∪ [3,∞) = {x : x ≤ 2 or x ≥ 3}.

This corresponds to option C (x ≤ 2 or x ≥ 3).