1. **State the problem:** Solve the equation $$4 - 9 + 2(n + 3) = 4n - 7$$ for $n$. 2. **Rewrite the equation:** Simplify the left side by distributing and combining like terms. $$4 - 9 + 2(n + 3) = 4n - 7$$ $$-5 + 2n + 6 = 4n - 7$$ $$(-5 + 6) + 2n = 4n - 7$$ $$1 + 2n = 4n - 7$$ 3. **Isolate variable terms:** Subtract $2n$ from both sides. $$1 + 2n - \cancel{2n} = 4n - 7 - \cancel{2n}$$ $$1 = 2n - 7$$ 4. **Isolate constant terms:** Add $7$ to both sides. $$1 + 7 = 2n - 7 + 7$$ $$8 = 2n$$ 5. **Solve for $n$:** Divide both sides by $2$. $$\frac{8}{\cancel{2}} = \frac{2n}{\cancel{2}}$$ $$4 = n$$ **Final answer:** $$n = 4$$