**Solve for \[a\].**
*Give an exact answer.*

\[3+0.5(4a+8)=9-2a\]

Let's solve the equation step by step:

Given equation:
\[
3 + 0.5(4a + 8) = 9 - 2a
\]

### Step 1: Distribute the 0.5 on the left-hand side.

\[
3 + 0.5 \times 4a + 0.5 \times 8 = 9 - 2a
\]
\[
3 + 2a + 4 = 9 - 2a
\]

### Step 2: Combine like terms on the left-hand side.

\[
(3 + 4) + 2a = 9 - 2a
\]
\[
7 + 2a = 9 - 2a
\]

### Step 3: Add \(2a\) to both sides to move the \(a\) terms to one side.

\[
7 + 2a + 2a = 9 - 2a + 2a
\]
\[
7 + 4a = 9
\]

### Step 4: Subtract 7 from both sides to isolate the \(a\)-term.

\[
4a = 9 - 7
\]
\[
4a = 2
\]

### Step 5: Divide both sides by 4 to solve for \(a\).

\[
a = \frac{2}{4}
\]
\[
a = \frac{1}{2}
\]

### Final Answer:
\[
a = \frac{1}{2}
\]

Would you like more details on any step? 

Here are 5 related questions:
1. How do you distribute constants over parentheses?
2. What are like terms, and why do we combine them?
3. How do you solve linear equations with variables on both sides?
4. Can you apply the same steps to solve equations with fractions?
5. How can you check the solution to an equation?

**Tip:** Always check your solution by substituting the value back into the original equation.

Solve for [a]. 3 + 0.5(4a + 8) = 9 - 2a. Give an exact answer.

Learn how to solve the linear equation 3 + 0.5(4a + 8) = 9 - 2a with a detailed step-by-step solution. This problem covers algebraic concepts such as the distributive property, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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