Solution - Absolute value equations

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-2x-4=2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-2x=2+4$$

Simplify the arithmetic:

$$-2x=6$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Move the negative sign from the denominator to the numerator:

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

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:

$$x=-3$$

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$4x-4=-2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$4x=-2+4$$

Simplify the arithmetic:

$$4x=2$$

Divide both sides by :

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

Simplify the fraction:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=\frac{1}{2}$$