To solve this equation, we need to consider two cases: when the expression inside the absolute value brackets is positive and when it's negative.

Case 1: 3 + x is positive
If 3 + x is positive, then the absolute value of 3 + x is equal to 3 + x. Therefore, the equation becomes:
1 + (3 + x) - 2 = 0
1 + 3 + x - 2 = 0
4 + x - 2 = 0
x + 2 = 0
x = -2

Case 2: 3 + x is negative
If 3 + x is negative, then the absolute value of 3 + x becomes its negation, -(3 + x). Therefore, the equation becomes:
1 + (-(3 + x)) - 2 = 0
1 - 3 - x - 2 = 0
-2 - x = 0
-x = 2
x = -2

Therefore, the solution to the equation |1 + |3 + x|| - 2 = 0 is x = -2.