Question

Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8 .(1 point)
Responses

83
Start Fraction 8 over 3 End Fraction

166
Start Fraction 16 over 6 End Fraction

4
4

12
12

1 answer

Let's solve the equation step by step:

Given the equation:

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

  1. First, combine the terms involving \(f\). Note that \(2f\) can be expressed with a common denominator of 5:

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

So, we rewrite the equation:

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

  1. Now combine the \(f\) terms:

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

This simplifies to:

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

  1. To eliminate the fractions, multiply every term in the equation by 5:

\[ 5\left(\frac{12f}{5}\right) - 5\left(\frac{8}{5}\right) = 5 \cdot 8 \]

This simplifies to:

\[ 12f - 8 = 40 \]

  1. Next, add 8 to both sides:

\[ 12f = 40 + 8 \]

\[ 12f = 48 \]

  1. Finally, divide both sides by 12:

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

Which simplifies to:

\[ f = 4 \]

Thus, the solution to the equation is:

\[ \boxed{4} \]