#### Answer

$a+b+|a-b|=2b$

#### Work Step by Step

$a+b+|a-b|,$ where $a\lt b$
Since $a\lt b$, the substraction inside the absolute value bars will result in a negative number. To express this quantity without the absolute value bars, we must change its sign. After that, simplify the resulting expression:
$a+b+|a-b|=a+b-(a-b)=a+b-a+b=2b$