  We prove a recent conjecture of Beisegel et al. that for every positive
integer k, every graph containing an induced P_k also contains an avoidable
P_k. Avoidability generalises the notion of simpliciality best known in the
context of chordal graphs. The conjecture was only established for k in {1,2}
(Ohtsuki et al. 1976, and Beisegel et al. 2019, respectively). Our result also
implies a result of Chv\'atal et al. 2002, which assumed cycle restrictions. We
provide a constructive and elementary proof, relying on a single trick
regarding the induction hypothesis. In the line of previous works, we discuss
conditions for multiple avoidable paths to exist.
