Kinetic Theory of Gases and molecular velocities of gases
Inelastic collisions are such collisions, that dissipate mechanical energy to other energy forms. It may be e.g. acoustic energy, light, thermal energy ( in macro context only ) or internal energy of an object.

The change of the internal energy in molecular context can be creation/breaking of chemical bonds, or changes of electron energy states. In usual conditions of stable enough gases, these events are very negligible, as average kinetic energy is much smaller than the energy needed to such a change.

Be aware that even fully elastic collision generally leads to a change of the mechanical energy of an object, in whole, or its translational, vibrational and rotational parts.

Imagine 2 identical balls moving at the same speed on a colliding course. After the collision, they have still identical speed if and only if their collision was symmetric. Otherwise 1 ball will slow down and the other ball will speed up.

The justification of the kinetic gas theory is the best shown on very good agreement of prediction and observed behavior of permanent gasses at normal conditions.