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Solve for $f$ . $\newline$ $2 - \frac{1}{4}f = f - \frac{3}{4}f + 3$ $\newline$ $f =$ __

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Solve equations with variables on both sides: fractional coefficients

Full solution

Q. Solve for

f

.

\newline

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

\newline

f =

__

Combine like terms: Combine like terms involving $f$ on the right side of the equation. $2 - \frac{1}{4}f = f - \frac{3}{4}f + 3$ $f - \frac{3}{4}f = (1 - \frac{3}{4})f = \frac{1}{4}f$
Rewrite equation with terms: Rewrite the equation with all $f$ terms on one side and constant terms on the other. $2 - \frac{1}{4}f = \frac{1}{4}f + 3$ To isolate $f$ , add $\frac{1}{4}f$ to both sides. $2 - \frac{1}{4}f + \frac{1}{4}f = \frac{1}{4}f + \frac{1}{4}f + 3$ $2 = \frac{1}{2}f + 3$
Isolate $f$ by subtraction: Isolate $f$ by subtracting $3$ from both sides. $\newline$ $2 - 3 = \frac{1}{2}f$ $\newline$ $-1 = \frac{1}{2}f$
Solve for f: Solve for f by multiplying both sides by $2$ . $\newline$ $-1 \times 2 = \frac{1}{2}f \times 2$ $\newline$ $-2 = f$

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