Solution - Absolute value equations

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-6=-6$$

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x-6=6$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$2x=6+6$$

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:

$$x=6$$