Absolute Value Equations - Worksheet 1

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.

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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.

מרכז ארצי למורים למתמטיקה בחינוך העל יסודי, 20 February 2013, Created with GeoGebra