Solve the equation for x: |2x - 5| = 9.

Model Answer & Options

Source: Extra Practice

x = 7 or x = -2

x = 7 only

x = 2 or x = -7

x = 14 or x = -4

Explanation

According to the definition of modulus, |a| = b implies a = b or a = -b. Applying this to |2x - 5| = 9: Case 1: 2x - 5 = 9 gives 2x = 14, so x = 7. Case 2: 2x - 5 = -9 gives 2x = -4, so x = -2. Both values satisfy the equation. Option B is incomplete. Option C has incorrect signs during transposition. Option D is incorrect calculation.

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