Solution - Absolute value equations

$$\left(-2x+4\right)=-4x-12$$

Add $$$$ to both sides:

$$\left(-2x+4\right)+4x=\left(-4x-12\right)+4x$$

Group like terms:

$$\left(-2x+4x\right)+4=\left(-4x-12\right)+4x$$

Simplify the arithmetic:

$$2x+4=\left(-4x-12\right)+4x$$

Group like terms:

$$2x+4=\left(-4x+4x\right)-12$$

Simplify the arithmetic:

$$2x+4=-12$$

Subtract $$$$ from both sides:

$$\left(2x+4\right)-4=-12-4$$

Simplify the arithmetic:

$$2x=-12-4$$

Simplify the arithmetic:

$$2x=-16$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{-16}{2}$$

Simplify the fraction:

$$x=\frac{-16}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-8·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-8$$

$$\left(-2x+4\right)=4x+12$$

Subtract $$$$ from both sides:

$$\left(-2x+4\right)-4x=\left(4x+12\right)-4x$$

Group like terms:

$$\left(-2x-4x\right)+4=\left(4x+12\right)-4x$$

Simplify the arithmetic:

$$-6x+4=\left(4x+12\right)-4x$$

Group like terms:

$$-6x+4=\left(4x-4x\right)+12$$

Simplify the arithmetic:

$$-6x+4=12$$

Subtract $$$$ from both sides:

$$\left(-6x+4\right)-4=12-4$$

Simplify the arithmetic:

$$-6x=12-4$$

Simplify the arithmetic:

$$-6x=8$$

Divide both sides by :

$$\frac{\left(-6x\right)}{-6}=\frac{8}{-6}$$

Cancel out the negatives:

$$\frac{6x}{6}=\frac{8}{-6}$$

Simplify the fraction:

$$x=\frac{8}{-6}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-8}{6}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-4·2\right)}{\left(3·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{-4}{3}$$