Question

Which of the following inequalities is equivalent to 3 ≥ x ≥ 2?

(a) x ≤ 3 and x ≥ 2
(b) x ≤ 2 and x ≥ 3
(c) x < 3 and x > 2
(d) x > 3 and x < 2

Answer 1

The equivalent inequality to 3 ≥ x ≥ 2 is x ≤ 3 and x ≥ 2.

Step-by-step explanation:

The equivalent inequality to 3 ≥ x ≥ 2 is (a) x ≤ 3 and x ≥ 2.

To understand why, let's break it down.

1. We have the inequality 3 ≥ x, which means that x can be any number less than or equal to 3.
2. We also have the inequality x ≥ 2, which means that x can be any number greater than or equal to 2.
3. Combining these two inequalities, we get x ≤ 3 and x ≥ 2, which means that x can be any number between 2 and 3, inclusive.

Therefore, the answer is (a) x ≤ 3 and x ≥ 2.