Solution - Absolute value equations

$$\left(f-6\right)-f=f-f$$

Group like terms:

$$\left(f-f\right)-6=f-f$$

Simplify the arithmetic:

$$-6=f-f$$

Simplify the arithmetic:

$$-6=0$$

The statement is false:

$$-6=0$$

$$\left(f-6\right)+f=-f+f$$

Group like terms:

$$\left(f+f\right)-6=-f+f$$

Simplify the arithmetic:

$$2f-6=-f+f$$

Simplify the arithmetic:

$$2f-6=0$$

Add $$$$ to both sides:

$$\left(2f-6\right)+6=0+6$$

Simplify the arithmetic:

$$2f=0+6$$

Simplify the arithmetic:

$$2f=6$$

Divide both sides by :

$$\frac{\left(2f\right)}{2}=\frac{6}{2}$$

Simplify the fraction:

$$f=\frac{6}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$f=3$$