Absolute value equations, step by step

An absolute value equation has two answers.

The question

Solve |3x − 15| = 3

3x − 15 = 3or3x − 15 = −3
3x − 15 = 3x = 6
3x − 15 = −3x = 4
x = 4orx = 6
  1. The bars mean the inside is 3 away from zero — so it is 3 OR it is −3. Split into two equations.
  2. Solve the first, 3x − 15 = 3: add 15 to both sides: 3x = 18, then divide by 3: x = 6.
  3. Solve the second, 3x − 15 = −3: add 15 to both sides: 3x = 12, then divide by 3: x = 4.
  4. So x = 4 or x = 6 — both answers.

How it works.

  1. 01

    The bars mean the inside is 3 away from zero — so it is 3 OR it is −3. Split into two equations.

  2. 02

    Solve the first, 3x − 15 = 3: add 15 to both sides: 3x = 18, then divide by 3: x = 6.

  3. 03

    Solve the second, 3x − 15 = −3: add 15 to both sides: 3x = 12, then divide by 3: x = 4.

  4. 04

    So x = 4 or x = 6 — both answers.