Solution - Absolute value equations

$$\left(z+9\right)=-z-3$$

Add $$$$ to both sides:

$$\left(z+9\right)+z=\left(-z-3\right)+z$$

Group like terms:

$$\left(z+z\right)+9=\left(-z-3\right)+z$$

Simplify the arithmetic:

$$2z+9=\left(-z-3\right)+z$$

Group like terms:

$$2z+9=\left(-z+z\right)-3$$

Simplify the arithmetic:

$$2z+9=-3$$

Subtract $$$$ from both sides:

$$\left(2z+9\right)-9=-3-9$$

Simplify the arithmetic:

$$2z=-3-9$$

Simplify the arithmetic:

$$2z=-12$$

Divide both sides by :

$$\frac{\left(2z\right)}{2}=\frac{-12}{2}$$

Simplify the fraction:

$$z=\frac{-12}{2}$$

Find the greatest common factor of the numerator and denominator:

$$z=\frac{\left(-6·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$z=-6$$

$$\left(z+9\right)=z+3$$

Subtract $$$$ from both sides:

$$\left(z+9\right)-z=\left(z+3\right)-z$$

Group like terms:

$$\left(z-z\right)+9=\left(z+3\right)-z$$

Simplify the arithmetic:

$$9=\left(z+3\right)-z$$

Group like terms:

$$9=\left(z-z\right)+3$$

Simplify the arithmetic:

$$9=3$$

The statement is false:

$$9=3$$