Question

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

Answer 1

To solve the equation

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

we start by simplifying the left side. First, distribute the \(0.5\) within the parentheses:

\[
0.5(4a + 8) = 0.5 \cdot 4a + 0.5 \cdot 8 = 2a + 4.
\]

Now, substitute this back into the equation:

\[
3 + 2a + 4 = 9 - 2a.
\]

Next, combine like terms on the left side:

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

Now, isolate the variable \(a\). Start by adding \(2a\) to both sides:

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

Next, subtract \(7\) from both sides:

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

Now, divide both sides by \(4\):

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

Thus, the solution is

\[
\boxed{\frac{1}{2}}.
\]