Solution - Absolute value equations

$$\left(-y+7\right)-y=\left(y-7\right)-y$$

Group like terms:

$$\left(-y-y\right)+7=\left(y-7\right)-y$$

Simplify the arithmetic:

$$-2y+7=\left(y-7\right)-y$$

Group like terms:

$$-2y+7=\left(y-y\right)-7$$

Simplify the arithmetic:

$$-2y+7=-7$$

Subtract $$$$ from both sides:

$$\left(-2y+7\right)-7=-7-7$$

Simplify the arithmetic:

$$-2y=-7-7$$

Simplify the arithmetic:

$$-2y=-14$$

Divide both sides by :

$$\frac{\left(-2y\right)}{-2}=\frac{-14}{-2}$$

Cancel out the negatives:

$$\frac{2y}{2}=\frac{-14}{-2}$$

Simplify the fraction:

$$y=\frac{-14}{-2}$$

Cancel out the negatives:

$$y=\frac{14}{2}$$

Find the greatest common factor of the numerator and denominator:

$$y=\frac{\left(7·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$y=7$$

$$\left(-y+7\right)=-y+7$$

Add $$$$ to both sides:

$$\left(-y+7\right)+y=\left(-y+7\right)+y$$

Group like terms:

$$\left(-y+y\right)+7=\left(-y+7\right)+y$$

Simplify the arithmetic:

$$7=\left(-y+7\right)+y$$

Group like terms:

$$7=\left(-y+y\right)+7$$

Simplify the arithmetic:

$$7=7$$