1. The problem asks us to find the lower and upper bounds for a number $r$ which, when rounded to the nearest integer, equals 28. 2. When rounding to the nearest integer, values are rounded down if less than the midpoint and rounded up if at or above the midpoint. 3. For the number 28, the midpoint between 27 and 28 is 27.5, and the midpoint between 28 and 29 is 28.5. 4. Therefore, the lower bound is $27.5$ because any number $r \geq 27.5$ rounded to the nearest integer could be 28. 5. The upper bound is not inclusive and is $28.5$ because values $r < 28.5$ round down to 28, but numbers $\geq 28.5$ round to 29. 6. This gives the inequality: $$27.5 \leq r < 28.5$$ 7. Hence, any $r$ in the interval $[27.5, 28.5)$ rounds to the nearest integer 28.