To solve the equation |2x-5|-x=7, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x-5 is positive
When 2x-5 is positive, the equation becomes (2x-5)-x=7.
Simplifying this equation, we get 2x-5-x=7, which is x-5=7.
Adding 5 to both sides, we have x=12.

Case 2: 2x-5 is negative
When 2x-5 is negative, the equation becomes -(2x-5)-x=7.
Simplifying this equation, we get -2x+5-x=7, which is -3x+5=7.
Subtracting 5 from both sides, we have -3x=2.
Dividing both sides by -3, we get x=-2/3.

Therefore, the solutions to the equation |2x-5|-x=7 are x=12 and x=-2/3.