1. The problem is to evaluate the expression $7x + 2y + \frac{x}{2}$ when $x=2$ and $y=4$. 2. The expression is a linear combination of $x$ and $y$ with an additional fractional term involving $x$. 3. Substitute the given values into the expression: $$7(2) + 2(4) + \frac{2}{2}$$ 4. Calculate each term: $$14 + 8 + 1$$ 5. Add the results: $$14 + 8 + 1 = 23$$ 6. Therefore, the value of the expression when $x=2$ and $y=4$ is $23$.