Solution - Absolute value equations

$$\left(x+4\right)=-2x-8$$

Add $$$$ to both sides:

$$\left(x+4\right)+2x=\left(-2x-8\right)+2x$$

Group like terms:

$$\left(x+2x\right)+4=\left(-2x-8\right)+2x$$

Simplify the arithmetic:

$$3x+4=\left(-2x-8\right)+2x$$

Group like terms:

$$3x+4=\left(-2x+2x\right)-8$$

Simplify the arithmetic:

$$3x+4=-8$$

Subtract $$$$ from both sides:

$$\left(3x+4\right)-4=-8-4$$

Simplify the arithmetic:

$$3x=-8-4$$

Simplify the arithmetic:

$$3x=-12$$

Divide both sides by :

$$\frac{\left(3x\right)}{3}=\frac{-12}{3}$$

Simplify the fraction:

$$x=\frac{-12}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-4·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=-4$$

$$\left(x+4\right)=2x+8$$

Subtract $$$$ from both sides:

$$\left(x+4\right)-2x=\left(2x+8\right)-2x$$

Group like terms:

$$\left(x-2x\right)+4=\left(2x+8\right)-2x$$

Simplify the arithmetic:

$$-x+4=\left(2x+8\right)-2x$$

Group like terms:

$$-x+4=\left(2x-2x\right)+8$$

Simplify the arithmetic:

$$-x+4=8$$

Subtract $$$$ from both sides:

$$\left(-x+4\right)-4=8-4$$

Simplify the arithmetic:

$$-x=8-4$$

Simplify the arithmetic:

$$-x=4$$

Multiply both sides by $$$$:

$$-x·-1=4·-1$$

Remove the one(s):

$$x=4·-1$$

Simplify the arithmetic:

$$x=-4$$