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

Responses
4
4
166
Start Fraction 16 over 6 End Fraction
83
Start Fraction 8 over 3 End Fraction
12

1 answer

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will first eliminate the fractions by multiplying the entire equation by 5.

  1. Multiply every term by 5: \[ 5 \left(\frac{2f}{5}\right) - 5 \left(\frac{8}{5}\right) + 5(2f) = 5(8) \]

    This simplifies to: \[ 2f - 8 + 10f = 40 \]

  2. Combine like terms: \[ (2f + 10f) - 8 = 40 \] \[ 12f - 8 = 40 \]

  3. Add 8 to both sides: \[ 12f - 8 + 8 = 40 + 8 \] \[ 12f = 48 \]

  4. Divide both sides by 12: \[ f = \frac{48}{12} \] \[ f = 4 \]

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