Consider the case .
means the distance between
and
is less than
units.
Hence the solution is in between and
.
Consider the case .
means the distance between
and
is greater than
units.
Hence the solution is outside of and
.
Observe the graph:
\The graph has one terminal of the line graph containing dot at .
The other terminal of the line graph containing dot at .
The solutions are between and
as well as
and
are included in the solution set.
Therefore the absolute function :
\ .
.
The absolute function is .
The absolute function is .