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

\[ g = 2. \]