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

Case 1: When 2x - 1 >= 0
This means that 2x - 1 is positive, so the absolute value bars can be removed.
Therefore, the equation becomes:
2x - 1 + 7 = 8
2x + 6 = 8
2x = 2
x = 1

Case 2: When 2x - 1 < 0
This means that 2x - 1 is negative, so it becomes -(2x - 1) when the bars are removed.
Therefore, the equation becomes:
-(2x - 1) + 7 = 8
-2x + 1 + 7 = 8
-2x + 8 = 8
-2x = 0
x = 0

So the solution to the equation is x = 1 or x = 0.