1. **Problem Statement:** Determine if equation D, $\frac{1}{2}x = x + \frac{1}{2}$, has one solution. 2. **Write the equation:** $$\frac{1}{2}x = x + \frac{1}{2}$$ 3. **Isolate terms:** Subtract $x$ from both sides: $$\frac{1}{2}x - x = \frac{1}{2}$$ 4. **Simplify the left side:** $$\frac{1}{2}x - 1x = \left(\frac{1}{2} - 1\right)x = -\frac{1}{2}x$$ So the equation becomes: $$-\frac{1}{2}x = \frac{1}{2}$$ 5. **Solve for $x$:** Multiply both sides by $-2$ to clear the fraction: $$x = -2 \times \frac{1}{2} = -1$$ 6. **Interpretation:** The equation has exactly one solution, $x = -1$. **Summary:** Equation D has one unique solution at $x = -1$.