1. **State the problem:** Solve the equation $$-\frac{1}{2} = 3 - \left(\frac{1}{2}x - 10\right)$$ for $x$ and write the answer in simplest form. 2. **Rewrite the equation:** $$-\frac{1}{2} = 3 - \frac{1}{2}x + 10$$ 3. **Combine like terms on the right side:** $$3 + 10 = 13$$ So the equation becomes: $$-\frac{1}{2} = 13 - \frac{1}{2}x$$ 4. **Isolate the term with $x$ by subtracting 13 from both sides:** $$-\frac{1}{2} - 13 = 13 - \frac{1}{2}x - 13$$ $$-\frac{1}{2} - 13 = -\frac{1}{2}x$$ 5. **Simplify the left side:** $$-\frac{1}{2} - 13 = -\frac{1}{2} - \frac{26}{2} = -\frac{27}{2}$$ So: $$-\frac{27}{2} = -\frac{1}{2}x$$ 6. **Solve for $x$ by dividing both sides by $-\frac{1}{2}$:** $$x = \frac{-\frac{27}{2}}{-\frac{1}{2}}$$ 7. **Simplify the division by multiplying by the reciprocal:** $$x = -\frac{27}{2} \times \cancel{\frac{-2}{1}}$$ The negatives cancel and the 2's cancel: $$x = 27$$ **Final answer:** $$\boxed{27}$$