1. **State the problem:** Solve the equation $$\frac{1}{2} - \frac{n + 1}{5} = -\frac{1}{2}$$. 2. **Rewrite the equation:** To eliminate fractions, find the least common denominator (LCD), which is 10. 3. **Multiply both sides by 10:** $$10 \times \left(\frac{1}{2} - \frac{n + 1}{5}\right) = 10 \times \left(-\frac{1}{2}\right)$$ 4. **Simplify each term:** $$10 \times \frac{1}{2} = 5$$ $$10 \times \frac{n + 1}{5} = 2(n + 1) = 2n + 2$$ $$10 \times -\frac{1}{2} = -5$$ 5. **Rewrite the equation:** $$5 - (2n + 2) = -5$$ 6. **Distribute the negative sign:** $$5 - 2n - 2 = -5$$ 7. **Combine like terms:** $$3 - 2n = -5$$ 8. **Isolate the variable term:** $$-2n = -5 - 3$$ $$-2n = -8$$ 9. **Divide both sides by -2:** $$n = \frac{-8}{-2} = 4$$ **Final answer:** $$n = 4$$