1. The problem states that the number $x$ is rounded to the nearest integer as 23. 2. When rounding to the nearest integer, the maximum error is half the distance between two consecutive integers, which is $0.5$. 3. This means $x$ could be any number within $0.5$ units above or below 23. 4. Therefore, the error interval for $x$ is given by: $$22.5 \leq x < 23.5$$ 5. This interval ensures that any number rounded to 23 will lie within this range. Final answer: $x \in [22.5, 23.5)$