Answer
$x=\dfrac12$
Work Step by Step
$|x+10|=|x-11|$
$x+10=x-11~~~~~~~~~~~\text{or}~~~~~~~~~~~~~x+10=-(x-11)$
$x-x=-10-11~~~~~~~~~\text{or}~~~~~~~~~~~~~x+10=-x+11$
$0=-21~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{or}~~~~~~~~~~~~~2x=1$
$\text{No Solution}~~~~~~~~~~~~~~~~~~~~~\text{or}~~~~~~~~~~~~~x=\dfrac12$
