Solution - Absolute value equations

$$\left(2y-9\right)-4y=\left(4y+9\right)-4y$$

Group like terms:

$$\left(2y-4y\right)-9=\left(4y+9\right)-4y$$

Simplify the arithmetic:

$$-2y-9=\left(4y+9\right)-4y$$

Group like terms:

$$-2y-9=\left(4y-4y\right)+9$$

Simplify the arithmetic:

$$-2y-9=9$$

Add $$$$ to both sides:

$$\left(-2y-9\right)+9=9+9$$

Simplify the arithmetic:

$$-2y=9+9$$

Simplify the arithmetic:

$$-2y=18$$

Divide both sides by :

$$\frac{\left(-2y\right)}{-2}=\frac{18}{-2}$$

Cancel out the negatives:

$$\frac{2y}{2}=\frac{18}{-2}$$

Simplify the fraction:

$$y=\frac{18}{-2}$$

Move the negative sign from the denominator to the numerator:

$$y=\frac{-18}{2}$$

Find the greatest common factor of the numerator and denominator:

$$y=\frac{\left(-9·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$y=-9$$

$$\left(2y-9\right)=-4y-9$$

Add $$$$ to both sides:

$$\left(2y-9\right)+4y=\left(-4y-9\right)+4y$$

Group like terms:

$$\left(2y+4y\right)-9=\left(-4y-9\right)+4y$$

Simplify the arithmetic:

$$6y-9=\left(-4y-9\right)+4y$$

Group like terms:

$$6y-9=\left(-4y+4y\right)-9$$

Simplify the arithmetic:

$$6y-9=-9$$

Add $$$$ to both sides:

$$\left(6y-9\right)+9=-9+9$$

Simplify the arithmetic:

$$6y=-9+9$$

Simplify the arithmetic:

$$6y=0$$

Divide both sides by the coefficient:

$$y=0$$