Significant confusion exists in the standard pedagogical presentations on the issue of 0(-) and 0(+) in the Laplace transform treatment for linear systems. Moreover, Lthorn and L- approaches have been shown to yield the same solution, even as the issue has been of resurgent interest in the literature. In this work, the accuracy of the L+ approach over the L- approach for chemical engineering applications is substantiated. The popular 0(-) convention of the Laplace transform or the L- approach are found to be inconsistent and incorrect for some nontrivial chemical process systems. This is due to the fact that their models cannot account for the initialization inconsistency revealed using physical reasoning of the Lthorn approach. The results are illustrated by two chemical engineering examples. Common issues in the literature are also addressed.