Solution - Absolute value equations

$$\left(n-9\right)+n=\left(-n+5\right)+n$$

Group like terms:

$$\left(n+n\right)-9=\left(-n+5\right)+n$$

Simplify the arithmetic:

$$2n-9=\left(-n+5\right)+n$$

Group like terms:

$$2n-9=\left(-n+n\right)+5$$

Simplify the arithmetic:

$$2n-9=5$$

Add $$$$ to both sides:

$$\left(2n-9\right)+9=5+9$$

Simplify the arithmetic:

$$2n=5+9$$

Simplify the arithmetic:

$$2n=14$$

Divide both sides by :

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

Simplify the fraction:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$n=7$$

$$\left(n-9\right)=n-5$$

Subtract $$$$ from both sides:

$$\left(n-9\right)-n=\left(n-5\right)-n$$

Group like terms:

$$\left(n-n\right)-9=\left(n-5\right)-n$$

Simplify the arithmetic:

$$-9=\left(n-5\right)-n$$

Group like terms:

$$-9=\left(n-n\right)-5$$

Simplify the arithmetic:

$$-9=-5$$

The statement is false:

$$-9=-5$$