1. **State the problem:** Simplify the expression $\frac{1}{2} x - 58.5$. 2. **Understand the expression:** This is a linear expression in terms of $x$, where $\frac{1}{2} x$ means half of $x$, and $-58.5$ is a constant subtracted from it. 3. **No further simplification is possible** unless a value for $x$ is given. The expression is already in its simplest form. 4. **If you want to evaluate for a specific $x$,** substitute the value of $x$ into the expression and calculate. **Final answer:** The simplified expression is $$\frac{1}{2} x - 58.5$$