Using the properties of equality, find the solution to the equation

$\frac {2f}{5}-\frac {8}{5}+2f=8$ (1 point)
$\frac {8}{3}$
12
$\frac {16}{6}$
$.4$

1 answer

To solve the equation

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

we start by simplifying the left-hand side. First, we convert \(2f\) into a fraction with a denominator of \(5\):

\[ 2f = \frac{10f}{5}. \]

Now substituting this back into the equation gives us

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

Next, we can combine the terms on the left side which have a common denominator of \(5\):

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

which simplifies to

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

To eliminate the fraction, we multiply both sides of the equation by \(5\):

\[ 12f - 8 = 40. \]

Next, we want to isolate \(12f\) on one side. To do this, we add \(8\) to both sides:

\[ 12f = 48. \]

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

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

The solution to the equation is

\[ \boxed{4}. \]

(Note: The given options were not used in finding the solution, as they were inconsistent with the derived answer \(f = 4\).)