Solution - Absolute value equations

$$\left(a-2\right)+a=\left(-a+2\right)+a$$

Group like terms:

$$\left(a+a\right)-2=\left(-a+2\right)+a$$

Simplify the arithmetic:

$$2a-2=\left(-a+2\right)+a$$

Group like terms:

$$2a-2=\left(-a+a\right)+2$$

Simplify the arithmetic:

$$2a-2=2$$

Add $$$$ to both sides:

$$\left(2a-2\right)+2=2+2$$

Simplify the arithmetic:

$$2a=2+2$$

Simplify the arithmetic:

$$2a=4$$

Divide both sides by :

$$\frac{\left(2a\right)}{2}=\frac{4}{2}$$

Simplify the fraction:

$$a=\frac{4}{2}$$

Find the greatest common factor of the numerator and denominator:

$$a=\frac{\left(2·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$a=2$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$-2=-2$$