Solution - Absolute value equations

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x+2=-12$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$2x=-12-2$$

Simplify the arithmetic:

$$2x=-14$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{-14}{2}$$

Simplify the fraction:

$$x=\frac{-14}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-7·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-7$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2=12$$

The statement is false:

$$2=12$$