In this work a unifying approach is presented that leads to bounds for the distance in natural norms between solutions belonging to different spaces, of well-posed linear variational problems with the same input data. This is done in a general hilbertian framework, and in this sense, well-known inequalities such as Céa 's or Babuška 's for coercive and non coercive problems are extended and/or refined, as mere by-products of this unified setting. More particularly such an approach gives rise to both an improvement and a generalization to the weakly coercive case, of second Strang's inequality for abstract coercive problems. Additionally several aspects specific to linear variational problems are the subject of a thorough analysis beforehand, which also allows for clarifications and further refinements about the concept of weak coercivity.