Absolute Value Equations - Worksheet 2

Topic:
Equations
In this worksheet, we investigate the number of solutions of equation of the form: │ax + b│= │cx + d│ Change the values of the parameters of the equation by dragging on the rulers accordingly. Follow the graph’s changes and with them the intersection points.
While changing the parameters, focus your attention on the following cases: A. When the parameter e = 0, we distinguish between two cases: │a│= │c│, a ≠ c and check the number of solutions of the equation. B. When the parameter e ≠ 0, we distinguish between two cases: │a│= │c│, a ≠ c and check the number of solutions of the equation. Try to prove algebraically why in specific cases there is only one solution for the equation, two solutions, infinite number of solutions, or there is no solution.