Solving absolute value equations, step by step
An absolute value equation has two answers because the bars mean distance.
The question
Solve |x − 5| = 7
x − 5 = 7orx − 5 = −7
x − 5 = 7→x = 12
x − 5 = −7→x = −2
x = −2orx = 12
- The bars mean the inside is 7 away from zero — so it is 7 OR it is −7. Split into two equations.
- Solve the first, x − 5 = 7: add 5 to both sides: x = 12.
- Solve the second, x − 5 = −7: add 5 to both sides: x = −2.
- So x = −2 or x = 12 — both answers.
How it works.
- 01
The bars mean the inside is 7 away from zero — so it is 7 OR it is −7. Split into two equations.
- 02
Solve the first, x − 5 = 7: add 5 to both sides: x = 12.
- 03
Solve the second, x − 5 = −7: add 5 to both sides: x = −2.
- 04
So x = −2 or x = 12 — both answers.