Solution - Absolute value equations

$$\left(2a-9\right)-a=\left(a-6\right)-a$$

Group like terms:

$$\left(2a-a\right)-9=\left(a-6\right)-a$$

Simplify the arithmetic:

$$a-9=\left(a-6\right)-a$$

Group like terms:

$$a-9=\left(a-a\right)-6$$

Simplify the arithmetic:

$$a-9=-6$$

Add $$$$ to both sides:

$$\left(a-9\right)+9=-6+9$$

Simplify the arithmetic:

$$a=-6+9$$

Simplify the arithmetic:

$$a=3$$

$$\left(2a-9\right)=-a+6$$

Add $$$$ to both sides:

$$\left(2a-9\right)+a=\left(-a+6\right)+a$$

Group like terms:

$$\left(2a+a\right)-9=\left(-a+6\right)+a$$

Simplify the arithmetic:

$$3a-9=\left(-a+6\right)+a$$

Group like terms:

$$3a-9=\left(-a+a\right)+6$$

Simplify the arithmetic:

$$3a-9=6$$

Add $$$$ to both sides:

$$\left(3a-9\right)+9=6+9$$

Simplify the arithmetic:

$$3a=6+9$$

Simplify the arithmetic:

$$3a=15$$

Divide both sides by :

$$\frac{\left(3a\right)}{3}=\frac{15}{3}$$

Simplify the fraction:

$$a=\frac{15}{3}$$

Find the greatest common factor of the numerator and denominator:

$$a=\frac{\left(5·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$a=5$$