If the powers are equal, and the bases (here, 3) are equal then the exponents must also be equal:

|2x - 5| = 3

Case 1: |2x - 5| = +(2x - 5)

In this case, the white equation above states:
2x - 5 = 3 and thus x = 4

Case 2: |2x - 5| = -(2x - 5)

In this case, the white equation above states:
-2x + 5 = 3 and thus x = 1

In summary, the original equation is solved by:

x = 1 or x = 2 or (in set notation): {1,2}