Solution - Absolute value equations

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-x+8=1$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$-x=1-8$$

Simplify the arithmetic:

$$-x=-7$$

Multiply both sides by $$$$:

$$-x·-1=-7·-1$$

Remove the one(s):

$$x=-7·-1$$

Simplify the arithmetic:

$$x=7$$

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$3x+8=-1$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$3x=-1-8$$

Simplify the arithmetic:

$$3x=-9$$

Divide both sides by :

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

Simplify the fraction:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-3$$