1. **State the problem:** Simplify the expression $2q + \frac{1}{2}$. 2. **Understand the expression:** The expression consists of two terms: $2q$ and $\frac{1}{2}$. These terms cannot be combined further because one contains the variable $q$ and the other is a constant. 3. **Final expression:** Since the terms are unlike, the simplified form remains: $$2q + \frac{1}{2}$$ This is the simplest form of the expression.