Which of the following is the solution set to |2x - 5| = 7?

• A. x = 6
• B. x = -1
• C. x = 5
• D. x = 6 or -1

Answer: (D)

When an absolute value equals a number, the inside expression can be either that number or its opposite. So |2x - 5| = 7 means two possibilities: 2x - 5 = 7 or 2x - 5 = -7.

Solving the first: 2x = 12, so x = 6.

Solving the second: 2x = -2, so x = -1.

Thus the solution set is x = 6 or x = -1. Check confirms both work: |2(6) - 5| = |12 - 5| = 7, and |2(-1) - 5| = |-2 - 5| = |-7| = 7. Other values don’t satisfy the equation because they don’t make the inside equal to ±7.