1. **State the problem:** We are given a triangle ABC with segment DE inside it, where AB = $11x - 25$ and DE = $4x + 1$. We need to find the length of DE. 2. **Identify the relationship:** Usually, in such problems, DE is parallel to AB and the triangles are similar, so the lengths are proportional. However, since no ratio or additional information is given, we assume the problem asks to express DE in terms of $x$ or find DE if $x$ is known. 3. **Given:** - $AB = 11x - 25$ - $DE = 4x + 1$ 4. **Find DE:** Since DE is already expressed as $4x + 1$, the problem likely wants DE in terms of $x$ or a numerical value if $x$ is known. 5. **Conclusion:** Without a value for $x$, DE = $4x + 1$. **Final answer:** $$DE = 4x + 1$$