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

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Answer 1

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

1. Combine like terms: Start by expressing \( 2f \) with a common denominator of 5. We can do this by rewriting \( 2f \) as \( \frac{10f}{5} \):

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

   Now combine the terms:

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

   This simplifies to:

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

2. Eliminate the fraction: Multiply both sides by 5 to eliminate the denominator:

   \[ 12f - 8 = 40 \]

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

   \[ 12f = 48 \]

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

   \[ f = 4 \]

So the solution to the equation is:

\[ \boxed{4} \]