Solution - Absolute value equations

$$\left(x-3\right)=-2·-x-2·3$$

Group like terms:

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

Multiply the coefficients:

$$\left(x-3\right)=2x-2·3$$

Simplify the arithmetic:

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-x-3=-6$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$-x=-6+3$$

Simplify the arithmetic:

$$-x=-3$$

Multiply both sides by $$$$:

$$-x·-1=-3·-1$$

Remove the one(s):

$$x=-3·-1$$

Simplify the arithmetic:

$$x=3$$

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

$$\left(x-3\right)=-2x-2·-3$$

Simplify the arithmetic:

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$3x-3=6$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$3x=6+3$$

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:

$$x=3$$