Every complicated inequality can be reduced to the sign analysis of a function: the zeros and the behaviour at the endpoints of the domain are the “ingredients” from which the solution is read off. For rational inequalities or for products one builds a sign table, intersects the existence conditions, and reads the result off the table.
We have already used this strategy in the examples of rational irrational inequalities, and we shall meet it again in Year 4 with derivatives, when sign analysis becomes the central tool for the study of a function.
Links
Topics: Unifying methods
Concepts: Existence conditions · Irrational inequality · Sign analysis · Sign table
Skills: Solving inequalities · Studying a function