Solution - Absolute value equations

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$3x-4=2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$3x=2+4$$

Simplify the arithmetic:

$$3x=6$$

Divide both sides by :

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

Simplify the fraction:

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

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:

$$x=2$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-x-4=-2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-x=-2+4$$

Simplify the arithmetic:

$$-x=2$$

Multiply both sides by $$$$:

$$-x·-1=2·-1$$

Remove the one(s):

$$x=2·-1$$

Simplify the arithmetic:

$$x=-2$$