Solution - Absolute value equations

$$\left(4x-4\right)-6x=\left(6x+4\right)-6x$$

Group like terms:

$$\left(4x-6x\right)-4=\left(6x+4\right)-6x$$

Simplify the arithmetic:

$$-2x-4=\left(6x+4\right)-6x$$

Group like terms:

$$-2x-4=\left(6x-6x\right)+4$$

Simplify the arithmetic:

$$-2x-4=4$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-2x=4+4$$

Simplify the arithmetic:

$$-2x=8$$

Divide both sides by :

$$\frac{\left(-2x\right)}{-2}=\frac{8}{-2}$$

Cancel out the negatives:

$$\frac{2x}{2}=\frac{8}{-2}$$

Simplify the fraction:

$$x=\frac{8}{-2}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-8}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-4·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-4$$

$$\left(4x-4\right)=-6x-4$$

Add $$$$ to both sides:

$$\left(4x-4\right)+6x=\left(-6x-4\right)+6x$$

Group like terms:

$$\left(4x+6x\right)-4=\left(-6x-4\right)+6x$$

Simplify the arithmetic:

$$10x-4=\left(-6x-4\right)+6x$$

Group like terms:

$$10x-4=\left(-6x+6x\right)-4$$

Simplify the arithmetic:

$$10x-4=-4$$

Add $$$$ to both sides:

$$\left(10x-4\right)+4=-4+4$$

Simplify the arithmetic:

$$10x=-4+4$$

Simplify the arithmetic:

$$10x=0$$

Divide both sides by the coefficient:

$$x=0$$