Solution - Absolute value equations

$$\left(x-8\right)=3x+3·2$$

Simplify the arithmetic:

$$\left(x-8\right)=3x+6$$

Subtract $$$$ from both sides:

$$\left(x-8\right)-3x=\left(3x+6\right)-3x$$

Group like terms:

$$\left(x-3x\right)-8=\left(3x+6\right)-3x$$

Simplify the arithmetic:

$$-2x-8=\left(3x+6\right)-3x$$

Group like terms:

$$-2x-8=\left(3x-3x\right)+6$$

Simplify the arithmetic:

$$-2x-8=6$$

Add $$$$ to both sides:

$$\left(-2x-8\right)+8=6+8$$

Simplify the arithmetic:

$$-2x=6+8$$

Simplify the arithmetic:

$$-2x=14$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Move the negative sign from the denominator to the numerator:

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

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-7$$

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

$$\left(x-8\right)=3·-x+3·-2$$

Group like terms:

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

Multiply the coefficients:

$$\left(x-8\right)=-3x+3·-2$$

Simplify the arithmetic:

$$\left(x-8\right)=-3x-6$$

Add $$$$ to both sides:

$$\left(x-8\right)+3x=\left(-3x-6\right)+3x$$

Group like terms:

$$\left(x+3x\right)-8=\left(-3x-6\right)+3x$$

Simplify the arithmetic:

$$4x-8=\left(-3x-6\right)+3x$$

Group like terms:

$$4x-8=\left(-3x+3x\right)-6$$

Simplify the arithmetic:

$$4x-8=-6$$

Add $$$$ to both sides:

$$\left(4x-8\right)+8=-6+8$$

Simplify the arithmetic:

$$4x=-6+8$$

Simplify the arithmetic:

$$4x=2$$

Divide both sides by :

$$\frac{\left(4x\right)}{4}=\frac{2}{4}$$

Simplify the fraction:

$$x=\frac{2}{4}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=\frac{1}{2}$$