Solution - Absolute value equations

$$\left(x-2\right)-3x=\left(3x+2\right)-3x$$

Group like terms:

$$\left(x-3x\right)-2=\left(3x+2\right)-3x$$

Simplify the arithmetic:

$$-2x-2=\left(3x+2\right)-3x$$

Group like terms:

$$-2x-2=\left(3x-3x\right)+2$$

Simplify the arithmetic:

$$-2x-2=2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-2x=2+2$$

Simplify the arithmetic:

$$-2x=4$$

Divide both sides by :

$$\frac{\left(-2x\right)}{-2}=\frac{4}{-2}$$

Cancel out the negatives:

$$\frac{2x}{2}=\frac{4}{-2}$$

Simplify the fraction:

$$x=\frac{4}{-2}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-4}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-2$$

$$\left(x-2\right)=-3x-2$$

Add $$$$ to both sides:

$$\left(x-2\right)+3x=\left(-3x-2\right)+3x$$

Group like terms:

$$\left(x+3x\right)-2=\left(-3x-2\right)+3x$$

Simplify the arithmetic:

$$4x-2=\left(-3x-2\right)+3x$$

Group like terms:

$$4x-2=\left(-3x+3x\right)-2$$

Simplify the arithmetic:

$$4x-2=-2$$

Add $$$$ to both sides:

$$\left(4x-2\right)+2=-2+2$$

Simplify the arithmetic:

$$4x=-2+2$$

Simplify the arithmetic:

$$4x=0$$

Divide both sides by the coefficient:

$$x=0$$