Modulus

“distinct” only applies to a and c, not b.

The condition |a − b| + |b − c| = |a − c| is the triangle equality case, which happens only when b lies between a and c (including endpoints). So mathematically, b ∈ [a, c] or [c, a].

Now since the question says a and c are distinct, it just ensures the interval is proper (not a single point). It does NOT restrict b from being equal to a or c.

So option 1 is still valid.