To simplify \( 7(499) \) using the Distributive Property, we can break down \( 499 \) into a more manageable expression. We can rewrite \( 499 \) as \( 500 - 1 \):
\[ 7(499) = 7(500 - 1) \]
Now, apply the Distributive Property:
\[ 7(500 - 1) = 7 \times 500 - 7 \times 1 \]
Calculating each part:
\[ 7 \times 500 = 3500 \] \[ 7 \times 1 = 7 \]
Now, we subtract the two results:
\[ 3500 - 7 = 3493 \]
Thus, \( 7(499) \) simplifies to:
\[ \boxed{3493} \]