Solve for x: ||x| - 2| = 3.

Model Answer & Options

Source: Extra Practice

x = 5 or x = -5

x = 5, -5, 1, -1

x = 1 or x = -1

No solution

Explanation

The outer modulus implies |x| - 2 = 3 or |x| - 2 = -3. Case 1: |x| - 2 = 3 => |x| = 5, which gives x = 5 or x = -5. Case 2: |x| - 2 = -3 => |x| = -1. Since a modulus cannot be negative, Case 2 provides no real solutions. Thus, only x = ±5 are correct. Option B is wrong because it incorrectly treats |x| = -1 as having solutions ±1. Option C is only the incorrect part of the logic.

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