Source: Extra Practice
Which of the following values of x does NOT satisfy the inequality (x + 1) / (x - 1) ≥ 1?
Options
Option A
x = 2
Option B
x = 5
Option C is correct
x = 0
Option D
x = 10
Explanation
Solve (x + 1) / (x - 1) - 1 ≥ 0 → (x + 1 - (x - 1)) / (x - 1) ≥ 0 → 2 / (x - 1) ≥ 0. For this to be true, the denominator (x - 1) must be positive, i.e., x - 1 > 0, which means x > 1. Among the options, x = 2, 5, and 10 are all greater than 1. However, x = 0 is less than 1, so it does not satisfy the inequality.