|2x+1/2| + |2x-3/2| =2

To solve this absolute value equation, we need to consider the two possible cases when the expressions inside the absolute value bars are positive or negative.

Case 1: When 2x + 1/2 is positive and 2x - 3/2 is positive
2x + 1/2 + 2x - 3/2 = 2
4x - 2 = 2
4x = 4
x = 1

Case 2: When 2x + 1/2 is negative and 2x - 3/2 is negative
-(2x + 1/2) - (2x - 3/2) = 2
-2x - 1/2 - 2x + 3/2 = 2
-4x + 1 = 2
-4x = 1
x = -1/4

Therefore, the solutions to the absolute value equation |2x+1/2| + |2x-3/2| = 2 are x = 1 and x = -1/4.