Solution - Linear equations with one unknown

$$\left(2+\frac{-1}{4}f\right)-\frac{1}{4}·f=\left(\frac{1}{4}f+3\right)-\frac{1}{4}f$$

Group like terms:

$$\left(\frac{-1}{4}·f+\frac{-1}{4}·f\right)+2=\left(\frac{1}{4}·f+3\right)-\frac{1}{4}f$$

Combine the fractions:

$$\frac{\left(-1-1\right)}{4}·f+2=\left(\frac{1}{4}·f+3\right)-\frac{1}{4}f$$

Combine the numerators:

$$\frac{-2}{4}·f+2=\left(\frac{1}{4}·f+3\right)-\frac{1}{4}f$$

Find the greatest common factor of the numerator and denominator:

$$\frac{\left(-1·2\right)}{\left(2·2\right)}·f+2=\left(\frac{1}{4}·f+3\right)-\frac{1}{4}f$$

Factor out and cancel the greatest common factor:

$$\frac{-1}{2}·f+2=\left(\frac{1}{4}·f+3\right)-\frac{1}{4}f$$

Group like terms:

$$\frac{-1}{2}·f+2=\left(\frac{1}{4}·f+\frac{-1}{4}f\right)+3$$

Combine the fractions:

$$\frac{-1}{2}·f+2=\frac{\left(1-1\right)}{4}f+3$$

Combine the numerators:

$$\frac{-1}{2}·f+2=\frac{0}{4}f+3$$

Reduce the zero numerator:

$$\frac{-1}{2}f+2=0f+3$$

Simplify the arithmetic:

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

$$\left(\frac{-1}{2}f+2\right)-2=3-2$$

Simplify the arithmetic:

$$\frac{-1}{2}f=3-2$$

Simplify the arithmetic:

$$\frac{-1}{2}f=1$$

$$\left(\frac{-1}{2}f\right)·\frac{2}{-1}=1·\frac{2}{-1}$$

Group like terms:

$$\left(\frac{-1}{2}·-2\right)f=1·\frac{2}{-1}$$

Multiply the coefficients:

$$\frac{\left(-1·-2\right)}{2}f=1·\frac{2}{-1}$$

Simplify the arithmetic:

$$1f=1·\frac{2}{-1}$$

$$f=1·\frac{2}{-1}$$

Simplify the arithmetic:

$$f=-2$$