Absolute value equations with coefficients, step by step
With a number in front of x, an absolute value equation adds one move to the split.
The question
Solve |3x + 9| = 6
3x + 9 = 6or3x + 9 = −6
3x + 9 = 6→x = −1
3x + 9 = −6→x = −5
x = −5orx = −1
- The bars mean the inside is 6 away from zero — so it is 6 OR it is −6. Split into two equations.
- Solve the first, 3x + 9 = 6: subtract 9 from both sides: 3x = −3, then divide by 3: x = −1.
- Solve the second, 3x + 9 = −6: subtract 9 from both sides: 3x = −15, then divide by 3: x = −5.
- So x = −5 or x = −1 — both answers.
How it works.
- 01
The bars mean the inside is 6 away from zero — so it is 6 OR it is −6. Split into two equations.
- 02
Solve the first, 3x + 9 = 6: subtract 9 from both sides: 3x = −3, then divide by 3: x = −1.
- 03
Solve the second, 3x + 9 = −6: subtract 9 from both sides: 3x = −15, then divide by 3: x = −5.
- 04
So x = −5 or x = −1 — both answers.