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 = 3→x = 6
3x − 15 = −3→x = 4
x = 4orx = 6
- The bars mean the inside is 3 away from zero — so it is 3 OR it is −3. Split into two equations.
- Solve the first, 3x − 15 = 3: add 15 to both sides: 3x = 18, then divide by 3: x = 6.
- Solve the second, 3x − 15 = −3: add 15 to both sides: 3x = 12, then divide by 3: x = 4.
- So x = 4 or x = 6 — both answers.
How it works.
- 01
The bars mean the inside is 3 away from zero — so it is 3 OR it is −3. Split into two equations.
- 02
Solve the first, 3x − 15 = 3: add 15 to both sides: 3x = 18, then divide by 3: x = 6.
- 03
Solve the second, 3x − 15 = −3: add 15 to both sides: 3x = 12, then divide by 3: x = 4.
- 04
So x = 4 or x = 6 — both answers.