Prompted by the evidence of international tests of achievement that Swedish students have poor equation solving skills, this paper presents an interview study of upper secondary students' understanding of the topic. Students, from both vocational and academic tracks in two typical suburban upper secondary schools were invited to explain how a solution to the algebraic equation x + 5 = 4x -1, presented with no explanation, had been conceptualised by the hidden solver. Analyses showed that students were not only familiar with linear equations but consistently invoked a 'do the same to both sides' procedure, indicating a secure understanding of the principles underpinning the solution of algebraic equations. Such understandings, which seem to defy international tests' outcomes are conceptually beyond a reliance on the inverse operations necessary for arithmetical equations. Explanations for this apparent inconsistency, which go beyond mere maturation, are proposed.