2011 AMC 10B Problem 3

At a store, when a length is reported as x inches that means the length is at least x - 0.5 inches and at most x + 0.5 inches. Suppose the dimensions of a rectangular tile are reported as 2 inches by 3 inches. In square inches, what is the minimum area for the rectangle?

\textbf{(A)}\ 3.75 \qquad\textbf{(B)}\ 4.5 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 8.75

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.