Which of the following describes all values of \(n\) for which \(n^2-1\ge 0.\)

[M7MBA]

Which of the following describes all values of \(n\) for which \(n^2-1\ge 0.\)

(A) \(n\ge 1\)
(B) \(n\le1\)
(C) \(0\le n \le 1\)
(D) \(n\le -1\) or \(n \ge 1\)
(E) \(-1\le n\le 1\)

Answer: D

Source: Veritas Prep

[Scott@TargetTestPrep]

Which of the following describes all values of \(n\) for which \(n^2-1\ge 0.\)

(A) \(n\ge 1\)
(B) \(n\le1\)
(C) \(0\le n \le 1\)
(D) \(n\le -1\) or \(n \ge 1\)
(E) \(-1\le n\le 1\)

Answer: D

Solution:

Simplifying, we have:

n^2 ≥ 1

√(n^2) ≥ √1

|n| ≥ 1

n ≥ 1 or -n ≥ 1 → n ≤ -1

Answer: D