Solution - Absolute value equations

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

Group like terms:

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

Simplify the arithmetic:

$$-3x+6=x-x$$

Simplify the arithmetic:

$$-3x+6=0$$

Subtract $$$$ from both sides:

$$\left(-3x+6\right)-6=0-6$$

Simplify the arithmetic:

$$-3x=0-6$$

Simplify the arithmetic:

$$-3x=-6$$

Divide both sides by :

$$\frac{\left(-3x\right)}{-3}=\frac{-6}{-3}$$

Cancel out the negatives:

$$\frac{3x}{3}=\frac{-6}{-3}$$

Simplify the fraction:

$$x=\frac{-6}{-3}$$

Cancel out the negatives:

$$x=\frac{6}{3}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=2$$

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

Group like terms:

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

Simplify the arithmetic:

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

Simplify the arithmetic:

$$-x+6=0$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$-x=0-6$$

Simplify the arithmetic:

$$-x=-6$$

Multiply both sides by $$$$:

$$-x·-1=-6·-1$$

Remove the one(s):

$$x=-6·-1$$

Simplify the arithmetic:

$$x=6$$