Question: Solve for $a$. Give an exact answer. $$3+0.5(4a+8)=9-2a$$
1. **State the problem:** Solve the equation $$3+0.5(4a+8)=9-2a$$ for the variable $a$.
2. **Write down the equation:** $$3 + 0.5(4a + 8) = 9 - 2a$$
3. **Distribute the $0.5$ inside the parentheses:**
$$3 + 0.5 \times 4a + 0.5 \times 8 = 9 - 2a$$
$$3 + 2a + 4 = 9 - 2a$$
4. **Combine like terms on the left side:**
$$3 + 4 + 2a = 9 - 2a$$
$$7 + 2a = 9 - 2a$$
5. **Add $2a$ to both sides to get all $a$ terms on one side:**
$$7 + 2a + 2a = 9 - 2a + 2a$$
$$7 + 4a = 9$$
6. **Subtract $7$ from both sides:**
$$7 + 4a - 7 = 9 - 7$$
$$4a = 2$$
7. **Divide both sides by $4$ to solve for $a$:**
$$a = \frac{2}{4}$$
8. **Simplify the fraction:**
$$a = \frac{\cancel{2}}{\cancel{4}} = \frac{1}{2}$$
**Final answer:** $$a = \frac{1}{2}$$