Solution - Absolute value equations

$$\left(-x+3\right)-2x=\left(2x+9\right)-2x$$

Group like terms:

$$\left(-x-2x\right)+3=\left(2x+9\right)-2x$$

Simplify the arithmetic:

$$-3x+3=\left(2x+9\right)-2x$$

Group like terms:

$$-3x+3=\left(2x-2x\right)+9$$

Simplify the arithmetic:

$$-3x+3=9$$

Subtract $$$$ from both sides:

$$\left(-3x+3\right)-3=9-3$$

Simplify the arithmetic:

$$-3x=9-3$$

Simplify the arithmetic:

$$-3x=6$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Move the negative sign from the denominator to the numerator:

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

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:

$$x=-2$$

$$\left(-x+3\right)=-2x-9$$

Add $$$$ to both sides:

$$\left(-x+3\right)+2x=\left(-2x-9\right)+2x$$

Group like terms:

$$\left(-x+2x\right)+3=\left(-2x-9\right)+2x$$

Simplify the arithmetic:

$$x+3=\left(-2x-9\right)+2x$$

Group like terms:

$$x+3=\left(-2x+2x\right)-9$$

Simplify the arithmetic:

$$x+3=-9$$

Subtract $$$$ from both sides:

$$\left(x+3\right)-3=-9-3$$

Simplify the arithmetic:

$$x=-9-3$$

Simplify the arithmetic:

$$x=-12$$