The expression "half the sum of $x$ and 3" can be written mathematically as:

$\frac{x + 3}{2}$

This represents the sum of $x$ and 3, divided by 2.

Would you like more details or have any questions?

Here are some related questions:

1. How do you simplify expressions like this?
2. What if you want to double the expression instead of halving it?
3. How does this expression change if you subtract 3 from $x$ instead of adding it?
4. Can you solve for $x$ if the expression equals a specific number?
5. How does the expression change if you multiply $x$ by a number before summing it with 3?

Tip: When dealing with algebraic expressions, always perform operations in the correct order (parentheses, exponents, multiplication/division, and addition/subtraction).