Solution - Absolute value equations

$$\left(n+8\right)-2n=\left(2n+1\right)-2n$$

Group like terms:

$$\left(n-2n\right)+8=\left(2n+1\right)-2n$$

Simplify the arithmetic:

$$-n+8=\left(2n+1\right)-2n$$

Group like terms:

$$-n+8=\left(2n-2n\right)+1$$

Simplify the arithmetic:

$$-n+8=1$$

Subtract $$$$ from both sides:

$$\left(-n+8\right)-8=1-8$$

Simplify the arithmetic:

$$-n=1-8$$

Simplify the arithmetic:

$$-n=-7$$

Multiply both sides by $$$$:

$$-n·-1=-7·-1$$

Remove the one(s):

$$n=-7·-1$$

Simplify the arithmetic:

$$n=7$$

$$\left(n+8\right)=-2n-1$$

Add $$$$ to both sides:

$$\left(n+8\right)+2n=\left(-2n-1\right)+2n$$

Group like terms:

$$\left(n+2n\right)+8=\left(-2n-1\right)+2n$$

Simplify the arithmetic:

$$3n+8=\left(-2n-1\right)+2n$$

Group like terms:

$$3n+8=\left(-2n+2n\right)-1$$

Simplify the arithmetic:

$$3n+8=-1$$

Subtract $$$$ from both sides:

$$\left(3n+8\right)-8=-1-8$$

Simplify the arithmetic:

$$3n=-1-8$$

Simplify the arithmetic:

$$3n=-9$$

Divide both sides by :

$$\frac{\left(3n\right)}{3}=\frac{-9}{3}$$

Simplify the fraction:

$$n=\frac{-9}{3}$$

Find the greatest common factor of the numerator and denominator:

$$n=\frac{\left(-3·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$n=-3$$