Solution - Absolute value equations

$$\left(z+17\right)-z=\left(z+17\right)-z$$

Group like terms:

$$\left(z-z\right)+17=\left(z+17\right)-z$$

Simplify the arithmetic:

$$17=\left(z+17\right)-z$$

Group like terms:

$$17=\left(z-z\right)+17$$

Simplify the arithmetic:

$$17=17$$

$$\left(z+17\right)=-z-17$$

Add $$$$ to both sides:

$$\left(z+17\right)+z=\left(-z-17\right)+z$$

Group like terms:

$$\left(z+z\right)+17=\left(-z-17\right)+z$$

Simplify the arithmetic:

$$2z+17=\left(-z-17\right)+z$$

Group like terms:

$$2z+17=\left(-z+z\right)-17$$

Simplify the arithmetic:

$$2z+17=-17$$

Subtract $$$$ from both sides:

$$\left(2z+17\right)-17=-17-17$$

Simplify the arithmetic:

$$2z=-17-17$$

Simplify the arithmetic:

$$2z=-34$$

Divide both sides by :

$$\frac{\left(2z\right)}{2}=\frac{-34}{2}$$

Simplify the fraction:

$$z=\frac{-34}{2}$$

Find the greatest common factor of the numerator and denominator:

$$z=\frac{\left(-17·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$z=-17$$