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

Answer 1

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

1. Clear the fractions by multiplying every term by 5:

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

   This simplifies to:

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

2. Combine like terms on the left side:

   \[ (2f + 10f) - 8 = 40 \] \[ 12f - 8 = 40 \]

3. Isolate the term with \( f \) by adding 8 to both sides:

   \[ 12f - 8 + 8 = 40 + 8 \] \[ 12f = 48 \]

4. Solve for \( f \) by dividing both sides by 12:

   \[ f = \frac{48}{12} \] \[ f = 4 \]

Thus, the solution to the equation is \( \boxed{4} \).