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Mobile-edge computing (MEC) is expected to provide low-latency computation service for wireless devices (WDs). However, when WDs are located at cell edge or communication links between base stations (BSs) and WDs are blocked, the offloading latency will be large. To address this issue, we propose an intelligent reflecting surface (IRS)-assisted cell-free MEC system consisting of multiple BSs and IRSs for improving the transmission environment. Consequently, we formulate a min-max latency optimization problem by jointly designing multi-user detection (MUD) matrices, IRSs' reflecting beamforming vectors, WDs' transmit power and edge computing resource, subject to constraints on edge computing capability and IRSs phase shifts. To solve it, an alternating optimization algorithm based on the block coordinate descent (BCD) technique is proposed, in which the original non-convex problem is decoupled into two subproblems for alternately optimizing computing and communication parameters. In particular, we optimize the MUD matrix based on the second-order cone programming (SOCP) technique, and then develop two efficient algorithms to optimize IRSs' reflecting vectors based on the semi-definite relaxation (SDR) and successive convex approximation (SCA) techniques, respectively. Numerical results show that employing IRSs in cell-free MEC systems outperforms conventional MEC systems, resulting in up to about 60% latency reduction can be attained. Moreover, numerical results confirm that our proposed algorithms enjoy a fast convergence, which is beneficial for practical implementation.