Solution - Absolute value equations

$$x=-x-4$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x=-4$$

Divide both sides by :

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

Simplify the fraction:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-2$$

$$x=x+4$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$0=\left(x+4\right)-x$$

Group like terms:

$$0=\left(x-x\right)+4$$

Simplify the arithmetic:

$$0=4$$

The statement is false:

$$0=4$$