#### Answer

From $5\frac{1}{4}\text{ mi}$ to $5\frac{3}{4}\text{ mi}$

#### Work Step by Step

The measurement is given to the nearest $\frac{1}{2}$ mile, so the error is $\pm\frac{1}{4}\text{ mi}$. Therefore, to find the range of values that the measurement represents, we must both subtract and add $\frac{1}{4}$ to the given value. $$5\frac{1}{2}+\frac{1}{4}=5\frac{3}{4}$$$$5\frac{1}{2}-\frac{1}{4}=5\frac{1}{4}$$ Therefore the range of values is from $5\frac{1}{4}\text{ mi}$ to $5\frac{3}{4}\text{ mi}$