Absolute value equation

Question

|1-X| = 2X-5

Answer 1

case 1:
1-x = 2x-5
-3x = -6
x = 2

case 2:

-1+x = 2x-5
-x = -4
x = 4

x = 2 or x = 4

but by definition of absolute value,
2x-5 ≥ 0
2x ≥5
x ≥ 5/2

so x = 4