Using the properties of equality, find the solution to the equation (2f)/5 - 8/5 + 2f = 8 (point) 12 8/3; 16/6

Answer 1

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we'll follow these steps.

1. Combine like terms: We can rewrite \( 2f \) as \( \frac{10f}{5} \) so we can combine it with \( \frac{2f}{5} \): \[ \frac{2f}{5} + \frac{10f}{5} = \frac{12f}{5} \] Thus, the equation becomes: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]

2. Eliminate fractions: Multiply through by \( 5 \) to eliminate the denominators: \[ 12f - 8 = 40 \]

3. Add 8 to both sides to isolate the term with \( f \): \[ 12f = 48 \]

4. Divide both sides by 12 to solve for \( f \): \[ f = 4 \]

So, the solution to the equation is: \[ f = 4 \]

If you meant to check against the numeric points provided (12, 8/3; 16/6), please clarify further. The solution based on solving the equation is purely \( f = 4 \).