If $a<b$, what is the value of $|a-b|+a+b$?

(Your answer can include $a$ and $b,$ and should be as simplified as possible.)
I notice that the expression inside the absolute value bars is $a-b,$ which is negative since $a<b.$ So, to make it positive, I need to multiply it by $-1.$ That means $|a-b|=-1(a-b)=-a+b.$ Now I can substitute this into the original expression and simplify: $|a-b|+a+b=(-a+b)+a+b=2b.$ 