Absolute Value Equations - Worksheet 1

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.
A. Let’s look at the cases in which │a│= │c│. What is the graphical meaning? How many solutions the equation has? Distinguish between three possible situations. B. Let’s assume now that a ≠ c. What is the graphical meaning? Pay attention to the case of one solution for the equation. Which case is it? Is there a case in which the equation has more than one solution? Is there a case in which the equation has infinite number of solutions? c. Try to explain algebraically the finding of A & B.