Solve |2x - 5| = 7.

• A. x = 6 or x = -1
• B. x = 5 or x = -2
• C. x = -6 or x = 1
• D. x = 7 or x = -3

Answer: (A)

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

Solve the first: 2x - 5 = 7 → 2x = 12 → x = 6.

Solve the second: 2x - 5 = -7 → 2x = -2 → x = -1.

Thus the solutions are x = 6 and x = -1. Check: for x = 6, |2(6) - 5| = |7| = 7; for x = -1, |2(-1) - 5| = |-7| = 7. Values that don’t make the inside equal to ±7 won’t satisfy the equation.