|2 - 4n| - 4 = 34
OA) {0,-1}
O B) {-9}
OC) {-8,4}
O D) {-9, 10)

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