The elementary reaction sequence A ↔ I → P is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfil the rate constants for the different approximations to hold. A graphical approach showing the behavior of the exact and approximate intermediate concentrations might help to clarify the use of these methods in the teaching of chemical kinetics. Finally, the previously acquired ideas on the approximate kinetic methods lead to the proposal that activated complexes in steady state rather than in quasi-equilibrium with the reactants might be a closer to reality alternative in the mathematical development of Transition State Theory (TST), leading to an expression for the rate constant of an elementary irreversible reaction that differs only in the factor 1-k (k being the transmission coefficient) with respect to that given by conventional TST, and to an expression for the equilibrium constant of an elementary reversible reaction more compatible with that predicted by chemical thermodynamics.