Simplifying Absolute Value Express the quantity without using absolute value.a+b+|a-b|,where a<b

Given:
The value of a is less than value of b.
Calculation:
The absolute value of a real number x is,
$\{\begin{array}{l}x,ifx\ge 0\\ -x,ifx<0\end{array}$
The value of a is less than b, so the subtraction will result in a negative value.
$|a-b|=-(a-b)=b-a$ (1)
Use the value of $|a-b|$ from equation (1), the quantiny $a+b+|a-b|$ is,
$a+b+|a-b|=a+b+b-a=2b$
The quantity $a+b+|a-b|$ without using the absolute value is 2b.