1. **Problem statement:** Given the segment lengths $XL = x + 7$ and $LV = 2x - 5$, find the length of $XY$. 2. **Understanding the problem:** Points $X$, $L$, and $V$ lie on the segment $XY$ such that $XL + LV = XY$. 3. **Formula used:** The length of the whole segment is the sum of its parts: $$XY = XL + LV$$ 4. **Substitute the given expressions:** $$XY = (x + 7) + (2x - 5)$$ 5. **Simplify the expression:** $$XY = x + 7 + 2x - 5 = (x + 2x) + (7 - 5) = 3x + 2$$ 6. **Final answer:** $$\boxed{XY = 3x + 2}$$