We present the results of a measurement of the spin-dependent asymmetry in 3→(e→,e′) inelastic scattering at kinematics on the low-energy transfer side of the quasielastic peak, including the region near the breakup threshold. Comparison with existing calculations based upon the plane wave impulse approximation shows significant deviation between the data and the model near the breakup threshold. Good agreement between data and theory is seen at higher energy transfer.