Solve the following equation
|2x+6|-7=40
Solve for x
|2x+6|-7 = 40
We add 7 to each side
|2x + 6| - 7 + 7 = 40 + 7
|2x + 6| = 47
Absolute Value Equations
Since this is an absolute value equation
Setup two equations
- 2x+6 = 47
- 2x+6 = -47
Solve Equation 1 → 2x+6 = 47
Subtract - 6 from both sides of the equation
2x+6 - 6= 47 - 6
2x = 41
Divide each side of absolute value equation 1 by 2
Keep our =
| 2x | |
| 2 |
| = |
| 41 |
| 2 |
Solution to absolute value equation 1 is
x = 20.5
Solve Equation 2 → 2x+6 = -47
Subtract - 6 from both sides of the equation
2x+6 - 6= -47 - 6
2x = - 53
Divide each side of absolute value equation 2 by 2
Keep our =
| 2x | |
| 2 |
| = |
| -53 |
| 2 |
Solution to absolute value equation 2 is
x = -26.5
