Solve the inequality 1 / |x - 3| < 1/2, where x ≠ 3.

Model Answer & Options

Source: Extra Practice

(-∞, 1) ∪ (5, ∞)

(1, 5)

(3, 5)

(-∞, 3) ∪ (3, 5)

Explanation

Given 1/|x - 3| < 1/2. Since the modulus is always positive for x ≠ 3, we can cross-multiply: 2 2. This implies x - 3 > 2 or x - 3 5 or x < 1. In interval notation, this is (-∞, 1) ∪ (5, ∞). Option B is for |x - 3| < 2. Options C and D do not cover both regions correctly.

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