Solution - Absolute value equations

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

Simplify the arithmetic:

$$0=\left(x-6\right)-x$$

Group like terms:

$$0=\left(x-x\right)-6$$

Simplify the arithmetic:

$$0=-6$$

The statement is false:

$$0=-6$$

$$x=-x+6$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$2x=\left(-x+6\right)+x$$

Group like terms:

$$2x=\left(-x+x\right)+6$$

Simplify the arithmetic:

$$2x=6$$

Divide both sides by :

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

Simplify the fraction:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=3$$