1. **State the problem:** We have a line segment divided into parts with lengths labeled as $x$, 11, 22, and the entire segment length is 32. 2. **Understand the segments:** The segment labeled 22 covers the middle and right parts, which means it includes the segment labeled 11 and the segment to the right of it. 3. **Set up the equation:** Since the entire segment length is 32, and the left segment is $x$, the middle segment is 11, and the combined middle and right segment is 22, we can write: $$x + 22 = 32$$ 4. **Solve for $x$:** $$x + 22 = 32$$ $$x = 32 - 22$$ $$x = 10$$ 5. **Check:** The sum of $x$ and 22 equals the total length 32, so $x = 10$ is correct. **Final answer:** $$x = 10$$