Answer:
D
Step-by-step explanation:
Given
| 2 - 4n | - 4 = 34 ( add 4 to both sides )
| 2 - 4n | = 38
The absolute value function always returns a positive value but the expression inside can be positive or negative, that is
2 - 4n = 38 OR -(2 - 4n) = 38
subtract 2 from both sides
- 4n = 36 ( divide both sides by - 4 )
n = - 9
OR
-(2 - 4n) = 38
- 2 + 4n = 38 ( add 2 to both sides )
4n = 40 ( divide both sides by 4 )
n = 10
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
n = - 9
| 2 + 36 | - 4 = | 38 | - 4 = 38 - 4 = 34 = right side
n = 10
| 2 - 40 | - 4 = | - 38 | - 4 = 38 - 4 = 34 = right side
Thus the solutions are { - 9, 10 } → D
