Solution - Absolute value equations

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

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:

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

Group like terms:

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

Simplify the arithmetic:

$$6=6$$

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

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:

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

Group like terms:

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

Simplify the arithmetic:

$$-2x+6=-6$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$-2x=-6-6$$

Simplify the arithmetic:

$$-2x=-12$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Cancel out the negatives:

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

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:

$$x=6$$