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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