Question

Using the properties of equality, solve the equation 1/4 * (8 - 16g) + 8 = g (point) The solution to the equation is g = Check answerRemaining Attempts 3

Answer 1

To solve the equation

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

let's follow these steps using the properties of equality.

1. **Distribute \(\frac{1}{4}\)**:

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

This simplifies to:

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

2. **Combine like terms**:

\[
10 - 4g = g
\]

3. **Add \(4g\) to both sides**:

\[
10 = g + 4g
\]

This simplifies to:

\[
10 = 5g
\]

4. **Divide both sides by 5**:

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

Simplifying gives:

\[
g = 2
\]

Now let's verify the solution by substituting \(g = 2\) back into the original equation.

Substituting \(g = 2\):

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

Calculating inside the parentheses first:

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

Since both sides are equal, the solution is verified.

Thus, the solution to the equation is

\[
g = 2.
\]