One-dimensional Hlawka inequality

For real numbers $a, b, c$: $|a+b|+|b+c|+|c+a| \le |a|+|b|+|c|+|a+b+c|$. The one-dimensional case of Hlawka's inequality; the base case for the proof that the sharp diagonal Hlawka constant of $\ell_2$ is $1$.