Solution - Absolute value equations

$$z-z=\left(z-4\right)-z$$

Simplify the arithmetic:

$$0=\left(z-4\right)-z$$

Group like terms:

$$0=\left(z-z\right)-4$$

Simplify the arithmetic:

$$0=-4$$

The statement is false:

$$0=-4$$

$$z=-z+4$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2z=4$$

Divide both sides by :

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

Simplify the fraction:

$$z=\frac{4}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$z=2$$