Tìm x, biết: |2x+1/2| + |2x-3/2| =2

To solve this equation, we need to consider the different cases for the absolute values.

Case 1: When both expressions inside the absolute values are positive:
2x + 1/2 + 2x - 3/2 = 2
4x - 1 = 2
4x = 3
x = 3/4

Case 2: When the first expression is positive and the second expression is negative:
2x + 1/2 - (2x - 3/2) = 2
2x + 1/2 - 2x + 3/2 = 2
1 + 2 = 2
3 = 2 (Not possible)

Case 3: When the first expression is negative and the second expression is positive:
-(2x + 1/2) + 2x - 3/2 = 2
-2x - 1/2 + 2x - 3/2 = 2
-2 = 2
-2 = 2 (Not possible)

Case 4: When both expressions inside the absolute values are 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 equation |2x+1/2| + |2x-3/2| = 2 are x = 3/4 and x = -1/4.