Solution - Absolute value equations

$$\left(x-12\right)-x=x-x$$

Group like terms:

$$\left(x-x\right)-12=x-x$$

Simplify the arithmetic:

$$-12=x-x$$

Simplify the arithmetic:

$$-12=0$$

The statement is false:

$$-12=0$$

$$\left(x-12\right)+x=-x+x$$

Group like terms:

$$\left(x+x\right)-12=-x+x$$

Simplify the arithmetic:

$$2x-12=-x+x$$

Simplify the arithmetic:

$$2x-12=0$$

Add $$$$ to both sides:

$$\left(2x-12\right)+12=0+12$$

Simplify the arithmetic:

$$2x=0+12$$

Simplify the arithmetic:

$$2x=12$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{12}{2}$$

Simplify the fraction:

$$x=\frac{12}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(6·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=6$$