Given their apparent simplicity to those who teach such things, absolute value equations and inequalities (the linear variety) have needlessly confounded a disproportionately high percentage of my College Algebra students throughout the years. In keeping with my ongoing quest to find the key to unlock the mystery which enshrouds this curiously impenetrable topic, I offer this GeoGebra worksheet.
As you use sliders to adjust the values of a, b, and c in either the inequalities |ax - b| <= c and
|ax - b| >= c or the equation |ax - b| = c, GeoGebra dynamically displays the graphs of y = |ax - b|, y = c, and their points of intersection. And it shades the solution set on the x-axis while simultaneously displaying the solution set using interval notation or listing notation as appropriate. Designed for use in the classroom, it also provides the enterprising student with a limitless collection of do-it-yourself examples, complete with solutions. Both the shading along the x-axis and the solution set notation can be turned on and off, so practice problems can be created and attempted before the instantaneous feedback is given.
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