Solution - Absolute value equations

$$x=2x+2·3$$

Simplify the arithmetic:

$$x=2x+6$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-x=6$$

Multiply both sides by $$$$:

$$-x·-1=6·-1$$

Remove the one(s):

$$x=6·-1$$

Simplify the arithmetic:

$$x=-6$$

$$x=2·\left(-x-3\right)$$

$$x=2·-x+2·-3$$

Group like terms:

$$x=\left(2·-1\right)x+2·-3$$

Multiply the coefficients:

$$x=-2x+2·-3$$

Simplify the arithmetic:

$$x=-2x-6$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$3x=-6$$

Divide both sides by :

$$\frac{\left(3x\right)}{3}=\frac{-6}{3}$$

Simplify the fraction:

$$x=\frac{-6}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-2·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=-2$$