Question

Use the properties of equality solve the equation 1/4(8-16g)+8=g

Answer 1

To solve the equation \( \frac{1}{4}(8 - 16g) + 8 = g \), we will follow these steps using the properties of equality.

1. Distribute \( \frac{1}{4} \) to the terms inside the parentheses:

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

This simplifies to:

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

2. Combine like terms on the left side:

\[
10 - 4g = g
\]

3. Add \( 4g \) to both sides to get all the \( g \) terms on one side:

\[
10 = g + 4g
\]

This simplifies to:

\[
10 = 5g
\]

4. Now, divide both sides by \( 5 \):

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

5. Thus, we find:

\[
g = 2
\]

To verify, substitute \( g = 2 \) back into the original equation:

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

Calculating the left side:

\[
\frac{1}{4}(8 - 32) + 8 = \frac{1}{4}(-24) + 8 = -6 + 8 = 2
\]

Both sides are equal, confirming our solution is correct.

The solution is:

\[
\boxed{2}
\]