Real Functions and Graphing Curves — Solving the absolute value equations and inequalities

About this lesson

This unit teaches students how to solve modulus (absolute value) equations and inequalities both graphically and algebraically. It begins by explaining that the solution set of an equation f(x)=g(x) is the set of x-coordinates of the intersection points of the two functions' graphs. Students learn to solve equations like |ax+b|=c by graphing the modulus function and a constant function, then finding intersection points, and also by using the piecewise definition of the modulus function. The unit also covers properties of absolute value, such as |ab|=|a||b| and |a+b|≤|a|+|b|, and then moves to solving inequalities like |x-a|<b or |x-a|>b, both graphically (by comparing curves) and algebraically (using rules like if |x|<a then -a<x<a). A real-life application involving temperature deviation is included. By the end, students should be able to solve modulus equations and inequalities using both methods and apply them to model problems.