Using the properties of equality find the solution to the equation 2f/5 - 8/5 + 2f = 8.

A) 4
B) 8/3
C) 12
D) 16/6

1 answer

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will first combine like terms and isolate \( f \).

  1. Rewrite \( 2f \) in terms of fifths to combine it with \( \frac{2f}{5} \): \[ 2f = \frac{10f}{5} \] Substituting this into the equation gives: \[ \frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8 \]

  2. Combine the terms with \( f \): \[ \frac{2f + 10f}{5} - \frac{8}{5} = 8 \] This simplifies to: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]

  3. To eliminate the fractions, multiply the entire equation by \( 5 \): \[ 5 \left( \frac{12f}{5} \right) - 5 \left( \frac{8}{5} \right) = 5 \times 8 \] Simplifying this yields: \[ 12f - 8 = 40 \]

  4. Now isolate \( 12f \) by adding \( 8 \) to both sides: \[ 12f = 40 + 8 \] \[ 12f = 48 \]

  5. Finally, solve for \( f \) by dividing both sides by \( 12 \): \[ f = \frac{48}{12} = 4 \]

The solution is \( f = 4 \).

So the answer is A) 4.