Solution
= Solution
The <triangle inequality> gives
$$
|a-b|=|(a-z)+(z-b)|\leq |z-a|+|z-b|.
$$
\b[Hence the left-hand side of the proposed equation is always at least $|a-b|$. There are no solutions when $c<|a-b|$.]
= Solution
The <triangle inequality> gives
$$
|a-b|=|(a-z)+(z-b)|\leq |z-a|+|z-b|.
$$
\b[Hence the left-hand side of the proposed equation is always at least $|a-b|$. There are no solutions when $c<|a-b|$.]