This IB Maths AA HL Topic AHL 2.15 – Solving Inequalities resource develops students’ confidence in solving inequalities of the form (g(x)\geq f(x)) using both analytical and graphical methods. It begins with the central idea that an inequality between two functions can be rewritten by moving all terms to one side and solving (g(x)-f(x)\geq 0). Students learn how to factor expressions, identify critical values, and use sign diagrams or test values to determine the correct solution intervals.

The lesson also connects algebraic solutions to graphical interpretation, with students identifying where one graph lies above or is equal to another and recognising that the relevant regions form the solution set. Practice includes quadratic and cubic inequalities, finding intersections, using technology for more complex functions, and following detailed TI-Nspire graphing instructions. Particular attention is given to the direction of the inequality and how reversing the comparison changes the solution. With clear explanations, worked examples, graphical tasks, calculator guidance, exam tips, and fully worked solutions, this resource helps HL students develop strong analytical and graphical inequality-solving skills in line with IB Mathematics AA expectations.