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

Responses

12
12

166
Start Fraction 16 over 6 End Fraction

83
Start Fraction 8 over 3 End Fraction

4
4

1 answer

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will follow the properties of equality.

  1. Combine like terms. We can rewrite \( 2f \) as \( \frac{10f}{5} \) to combine it with \( \frac{2f}{5} \): \[ \frac{2f}{5} + \frac{10f}{5} - \frac{8}{5} = 8 \]

    This simplifies to: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]

  2. Clear the fractions by multiplying every term by 5: \[ 5 \left( \frac{12f}{5} \right) - 5 \left( \frac{8}{5} \right) = 5 \times 8 \] This simplifies to: \[ 12f - 8 = 40 \]

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

  4. Divide by 12: \[ f = \frac{48}{12} \] This simplifies to: \[ f = 4 \]

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

Final Answer: 4