well the absolute value of something means that it could have possibly been a negative answer. so |x-3| = 14 could be
x - 3 = 14
or
x - 3 = - 14 (this is usually written -(x-3) = 14)
so we solve both of these
x - 3 = 14
x = 17
and
x - 3 = -14
x = -11
to shiw its the same i will do other way
-(x - 3) = 14
-x + 3 = 14
-x = 11
x = - 11