Using the properties of equality, solve the equation $\frac {1}{4}(8-16g)+8=g$

(1 point)
The solution to the equation is $g=$

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
11 days ago

To solve the equation

\[
\frac{1}{4}(8 - 16g) + 8 = g,
\]

we first simplify the left side of the equation.

Start by distributing \(\frac{1}{4}\) into the expression \(8 - 16g\):

\[
\frac{1}{4}(8) - \frac{1}{4}(16g) = 2 - 4g.
\]

Now, replace \(\frac{1}{4}(8 - 16g)\) in the original equation:

\[
2 - 4g + 8 = g.
\]

Next, combine the constant terms on the left side:

\[
10 - 4g = g.
\]

Now, we will isolate \(g\). First, add \(4g\) to both sides of the equation:

\[
10 = g + 4g,
\]

which simplifies to:

\[
10 = 5g.
\]

Next, divide both sides by \(5\):

\[
g = \frac{10}{5} = 2.
\]

Thus, the solution to the equation is

\[
\boxed{2}.
\]