Solve for f.

2–1/4f=f–3/4f+3

1 answer

To solve for \( f \) in the equation

\[ 2 - \frac{1}{4}f = f - \frac{3}{4}f + 3, \]

first simplify the right side:

\[ f - \frac{3}{4}f = \frac{4}{4}f - \frac{3}{4}f = \frac{1}{4}f. \]

Now, replace that in the equation:

\[ 2 - \frac{1}{4}f = \frac{1}{4}f + 3. \]

Next, get all the terms involving \( f \) on one side and constant terms on the other side. First, add \( \frac{1}{4}f \) to both sides:

\[ 2 = \frac{1}{4}f + \frac{1}{4}f + 3. \]

This simplifies to:

\[ 2 = \frac{2}{4}f + 3. \]

Now simplify \( \frac{2}{4}f \) to \( \frac{1}{2}f \):

\[ 2 = \frac{1}{2}f + 3. \]

Next, subtract 3 from both sides:

\[ 2 - 3 = \frac{1}{2}f, \]

which simplifies to:

\[ -1 = \frac{1}{2}f. \]

Now, multiply both sides by 2 to solve for \( f \):

\[ f = -2. \]

Thus, the solution is:

\[ \boxed{-2}. \]