Using the properties of equality, find the solution to the equation 2f/5 - 8/5 + 2f= 8 A) 8/3 B) 12 C) 4 D) 16/6

Answer 1

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we'll start by eliminating the fractions to make the equation easier to handle.

1. First, let's multiply the entire equation by 5 to eliminate the denominators:

\[ 5 \left( \frac{2f}{5} \right) - 5 \left( \frac{8}{5} \right) + 5 \cdot 2f = 5 \cdot 8 \]

This simplifies to:

\[ 2f - 8 + 10f = 40 \]

2. Combine like terms:

\[ 12f - 8 = 40 \]

3. Next, add 8 to both sides to isolate the term with \( f \):

\[ 12f = 40 + 8 \]

\[ 12f = 48 \]

4. Finally, divide both sides by 12 to solve for \( f \):

\[ f = \frac{48}{12} \]

\[ f = 4 \]

So the solution is:

C) 4