We need to solve the equation for \( a \):

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

### Step 1: Distribute the \( 0.5 \) on the left-hand side
Distribute the \( 0.5 \) across \( 4a \) and \( 8 \):

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

### Step 2: Combine like terms on the left-hand side
\[
(3 + 4) + 2a = 9 - 2a
\]
\[
7 + 2a = 9 - 2a
\]

### Step 3: Move all terms involving \( a \) to one side of the equation
Add \( 2a \) to both sides:
\[
7 + 2a + 2a = 9
\]
\[
7 + 4a = 9
\]

### Step 4: Isolate the variable term
Subtract 7 from both sides:
\[
4a = 9 - 7
\]
\[
4a = 2
\]

### Step 5: Solve for \( a \)
Divide both sides by 4:
\[
a = \dfrac{2}{4}
\]
\[
a = \dfrac{1}{2}
\]

### Final Answer:
The solution is \( a = \dfrac{1}{2} \).

Do you want further details on any of these steps or have any questions? Here are five related questions you might find interesting:

1. How do you handle equations where the distribution involves negative coefficients?
2. What changes if the equation includes decimals instead of fractions?
3. How would you solve this problem if there were more terms involving \( a \)?
4. Can you verify the solution by plugging it back into the original equation?
5. How do you simplify expressions when the terms involve different variables?

**Tip**: When distributing constants across terms inside parentheses, make sure to multiply every term, even if some terms are constants without variables.

Learn how to solve the linear equation 3 + 0.5(4a + 8) = 9 - 2a with a detailed step-by-step solution. This problem involves equations, the distributive property, combining like terms, and solving linear equations. Suitable for students in Grades 7-9.

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