Given the definition of the absolute value function, there are two possibilities for the next step.
Rember that |x| = x when x is positive and |x| is - x when x is negative.
So, these are the two possibilities for |x - 2| = 4
1) When the content inside the absolute value is positive, you can state x - 2 = 4
2) When the content inside the absolute value is negative you can state x - 2 = - 4.
So, the answer is
x - 2 = 4 and x - 2 = - 4.
I found this list of choices for this question:
a. x + 2 = −4
b. −x − 2 = 4
c. x + 2 = 4
d. x − 2 = −4
In that list , the only right is x - 2 = - 4, so choose it.
Answer: option d. x - 2 = - 4
