To solve the equation |2x-5|-x=7, we can break it down into two cases based on the absolute value.

Case 1: 2x-5 is positive (2x-5 > 0)
In this case, the absolute value can be removed, so the equation becomes:
(2x-5)-x=7
Simplifying, we have:
2x-5-x=7
x-5=7
Adding 5 to both sides, we get:
x=12

Case 2: 2x-5 is negative (2x-5 < 0)
In this case, the absolute value becomes its opposite, so the equation becomes:
-(2x-5)-x=7
Simplifying, we have:
-2x+5-x=7
-3x+5=7
Subtracting 5 from both sides, we get:
-3x=2
Dividing by -3, we have:
x=-2/3

Therefore, the solution to the equation |2x-5|-x=7 is x=12 or x=-2/3.