Solution - Absolute value equations

$$\left(-a+10\right)-a=\left(a-10\right)-a$$

Group like terms:

$$\left(-a-a\right)+10=\left(a-10\right)-a$$

Simplify the arithmetic:

$$-2a+10=\left(a-10\right)-a$$

Group like terms:

$$-2a+10=\left(a-a\right)-10$$

Simplify the arithmetic:

$$-2a+10=-10$$

Subtract $$$$ from both sides:

$$\left(-2a+10\right)-10=-10-10$$

Simplify the arithmetic:

$$-2a=-10-10$$

Simplify the arithmetic:

$$-2a=-20$$

Divide both sides by :

$$\frac{\left(-2a\right)}{-2}=\frac{-20}{-2}$$

Cancel out the negatives:

$$\frac{2a}{2}=\frac{-20}{-2}$$

Simplify the fraction:

$$a=\frac{-20}{-2}$$

Cancel out the negatives:

$$a=\frac{20}{2}$$

Find the greatest common factor of the numerator and denominator:

$$a=\frac{\left(10·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$a=10$$

$$\left(-a+10\right)=-a+10$$

Add $$$$ to both sides:

$$\left(-a+10\right)+a=\left(-a+10\right)+a$$

Group like terms:

$$\left(-a+a\right)+10=\left(-a+10\right)+a$$

Simplify the arithmetic:

$$10=\left(-a+10\right)+a$$

Group like terms:

$$10=\left(-a+a\right)+10$$

Simplify the arithmetic:

$$10=10$$