# Prove this inequality involving metrics

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## Main Question or Discussion Point

For any metric $(X, \rho)$ and points therein, prove that $|\rho(x, z) - \rho(y, u)| \leq \rho(x, y) + \rho(z, u)$.

I know that this will involve iterated applications of the triangle inequality...but I still need another hint on how to proceed.