Solution - Absolute value equations

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

$$2x+6=\left(-x-12\right)+x$$

Group like terms:

$$2x+6=\left(-x+x\right)-12$$

Simplify the arithmetic:

$$2x+6=-12$$

Subtract $$$$ from both sides:

$$\left(2x+6\right)-6=-12-6$$

Simplify the arithmetic:

$$2x=-12-6$$

Simplify the arithmetic:

$$2x=-18$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{-18}{2}$$

Simplify the fraction:

$$x=\frac{-18}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-9·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-9$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$6=12$$

The statement is false:

$$6=12$$