How do you solve | p-1| = 4 in a absolute value equation

Under a sign of absolute value can stay positive or negative number.
If it is a positive number then the its absolute value is a number.

1) p-1=4
p=4+1
p=5

If it is a negative number then the its absolute value is a opposite of a number.

2) -(p-1)=4
-p+1=4
-p=4-1
-p=3
p=-3

So, this equation has 2 roots p=5, and p=-3.

Check:
|p-1|=4
|5-1|=4
|4|=4
4=4 True

|p-1|=4
|-3-1|=4
|-4|=4
4=4 True

The answer would be a