Solution - Absolute value equations

$$3x=-x+2$$

Add $$$$ to both sides:

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

Simplify the arithmetic:

$$4x=\left(-x+2\right)+x$$

Group like terms:

$$4x=\left(-x+x\right)+2$$

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:

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

$$3x=x-2$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x=-2$$

Divide both sides by :

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

Simplify the fraction:

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

Simplify the fraction:

$$x=-1$$