Question

using the properties of equality, solve the equation 1 over 4(8-16g) + 8=g

Answer 1

To solve the equation \(\frac{1}{4}(8 - 16g) + 8 = g\), we will apply the properties of equality step by step.

1. Start with the original equation:
\[
\frac{1}{4}(8 - 16g) + 8 = g
\]

2. Simplify the fraction. Distributing \(\frac{1}{4}\):
\[
\frac{1}{4} \cdot 8 - \frac{1}{4} \cdot 16g + 8 = g
\]
This simplifies to:
\[
2 - 4g + 8 = g
\]
Combine the constants (2 and 8):
\[
10 - 4g = g
\]

3. Now, isolate \(g\). Add \(4g\) to both sides:
\[
10 = g + 4g
\]
Which simplifies to:
\[
10 = 5g
\]

4. Divide both sides by 5 to solve for \(g\):
\[
g = \frac{10}{5}
\]
Thus:
\[
g = 2
\]

5. To confirm, substitute \(g = 2\) back into the original equation:
\[
\frac{1}{4}(8 - 16(2)) + 8 \stackrel{?}{=} 2
\]
Calculate inside the parentheses:
\[
\frac{1}{4}(8 - 32) + 8 = \frac{1}{4}(-24) + 8 = -6 + 8 = 2
\]
Since both sides are equal, our solution is verified.

The solution to the equation is:
\[
\boxed{2}
\]