Using the properties of equality, find the solution to the equation \frac{2f}{5}-\frac{8}{5}+2f=8.(1 point) Responses 12 12 4 4 \frac{16}{6} Start Fraction 16 over 6 End Fraction \frac{8}{3}

Answer 1

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

1. First, combine like terms. Rewrite \(2f\) as \(\frac{10f}{5}\) to get a common denominator:

   \[ \frac{2f}{5} + \frac{10f}{5} - \frac{8}{5} = 8 \]

   This simplifies to:

   \[ \frac{12f - 8}{5} = 8 \]

2. To eliminate the fraction, multiply both sides by 5:

   \[ 12f - 8 = 40 \]

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

   \[ 12f = 48 \]

4. Finally, divide both sides by 12:

   \[ f = 4 \]

Thus, the solution to the equation is \(f = 4\).

So, the response is 4.