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using the properties of equality find the solution to the equation.

2f over 5- 8 over 5 + 2f=8

1 answer

To solve the equation \(\frac{2f}{5} - \frac{8}{5} + 2f = 8\), let's begin by simplifying the equation step-by-step.

  1. Combine like terms: First, let's focus on expressing \(2f\) with a common denominator. We can write \(2f\) as \(\frac{10f}{5}\).

    The equation now looks like this:

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

  2. Combine the fractions on the left:

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

    This simplifies to:

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

  3. Eliminate the fraction: Multiply both sides of the equation by 5 to eliminate the fraction:

    \[ 12f - 8 = 40 \]

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

    \[ 12f = 48 \]

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

    \[ f = 4 \]

Thus, the solution to the equation is:

\[ \boxed{4} \]