We report magnetic-susceptibility, specific-heat, and Raman-scattering investigations of alpha-TeVO4 containing V-O edge-sharing chains. These chains promote a system of ferromagnetic/antiferromagnetic spin-1/2 Heisenberg alternating exchange chains with pronounced spin frustration. The magnetic susceptibility and Raman scattering evidence a crossover at T*=85 K with different slopes of the reciprocal susceptibility and a magnetic phase transition into a long-range-ordered state at T-c=16 K. From Raman-scattering data a strong mutual coupling between lattice and magnetic degrees of freedom is deduced. A comparison to model calculations and prior Raman scattering on other chain systems yields a plausible interpretation of the microscopic mechanism for the crossover behavior.