In many School Certificate courses of Algebra inequalities are scarcely mentioned, and yet in Higher School Certificate work it is often assumed that the pupil can, without any further teaching, carry out easy manipulations of inequalities. It is true that the gap is a small one, but even the most intelligent pupils may fail to bridge it satisfactorily for themselves, and difficulties will then arise. One example of such a difficulty is noted in the Report of the Mathematical Association on the Teaching of Mechanics in the section on friction. The Report reads “There is a tendency among some pupils to proceed at once to the limiting case when equilibrium is about to be broken, to write down the equations for this case, manipulate them, and finally change the resulting equality into an inequality, using > or <, according to the answer required.”