2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67868We establish an inequality involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, we prove and refine a result by Goto and Nakamura, conjectured by Watanabe and Yoshida, which states that the Hilbert-Samuel multiplicity of a parameter ideal is greater than or equal to the colength of the tight closure of the ideal.8 pages, to appear in Bull. London Math. SocCommutative Algebra13D40; 13A35; 13H15text