Which of the following values of x does NOT satisfy the inequality (x + 1) / (x - 1) ≥ 1?

Model Answer & Options

Source: Extra Practice

x = 2

x = 5

x = 0

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.

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