The inequality is .
Use the Alternate Triangle Inequality: .
Write the inequalityin the form of Alternate Triangle Inequality.
\ (Form of Alternate Triangle Inequality)
(Distributive property:
)
(Apply additive inverse property:
)
(Add:
)
(Substitute:
)
(Rewrite the inequality)
Check the inequality.
\Case(i): and
(Original inequality)
(Substitute
)
(Substitute:
and
)
(Substitute:
and
)
(Subtract:
)
Case(i):
(Original inequality)
(Substitute
)
(Substitute:
and
)
(Substitute:
and
)
(Subtract:
)
Therefore, the solution is .
The solution is .