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

Question

Responses

16/6

12

8/3

4

Answer 1

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

1. Combine like terms: First, let's write \( 2f \) in terms of fractions with a common denominator. The common denominator here is 5.

   We can express \( 2f \) as \( \frac{10f}{5} \) (since \( 2f = \frac{10f}{5} \)).

   Now we can rewrite the equation:

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

2. Combine the fractions on the left side:

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

   This simplifies to:

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

3. Clear the fraction: Multiply both sides by 5 to eliminate the fraction:

   \[ 12f - 8 = 40 \]

4. Add 8 to both sides:

   \[ 12f = 48 \]

5. Divide both sides by 12:

   \[ f = 4 \]

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

The correct response is 4.