Solution - Absolute value equations

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x+8=2$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$2x=2-8$$

Simplify the arithmetic:

$$2x=-6$$

Divide both sides by :

$$\frac{\left(2x\right)}{2}=\frac{-6}{2}$$

Simplify the fraction:

$$x=\frac{-6}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-3$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$8=-2$$

The statement is false:

$$8=-2$$