Solution - Absolute value equations

$$\left(y-12\right)+y=\left(-y+12\right)+y$$

Group like terms:

$$\left(y+y\right)-12=\left(-y+12\right)+y$$

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2y-12=12$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$2y=12+12$$

Simplify the arithmetic:

$$2y=24$$

Divide both sides by :

$$\frac{\left(2y\right)}{2}=\frac{24}{2}$$

Simplify the fraction:

$$y=\frac{24}{2}$$

Find the greatest common factor of the numerator and denominator:

$$y=\frac{\left(12·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$y=12$$

$$\left(y-12\right)=y-12$$

Subtract $$$$ from both sides:

$$\left(y-12\right)-y=\left(y-12\right)-y$$

Group like terms:

$$\left(y-y\right)-12=\left(y-12\right)-y$$

Simplify the arithmetic:

$$-12=\left(y-12\right)-y$$

Group like terms:

$$-12=\left(y-y\right)-12$$

Simplify the arithmetic:

$$-12=-12$$