Solve the equation |x + 3| = 7.

• A. x = -4 or x = 10
• B. x = 3 or x = -10
• C. x = -3 or x = 7
• D. x = 4 or x = -10

Answer: (D)

Absolute value represents distance from zero. So |x+3| = 7 means x+3 is either 7 or -7. Solve both possibilities: x+3 = 7 gives x = 4, and x+3 = -7 gives x = -10. Therefore the solutions are 4 and -10, which you can check by substitution: |4+3| = 7 and |-10+3| = 7. Numbers that don’t satisfy those two cases won’t work (for example, x = -4 gives |-4+3| = 1, not 7).