Law of Trichotomy Applied to Absolute Value Inequalities in One Variable Part VII

Share Cognitive Science Implications for Teaching Mathematics
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Example: Solve the equality 

Discussion and Solution:  We begin by focusing not on the given equality, but on the “less than” inequality      which we immediately convert to the equivalent compound inequality and solve with normal techniques.

The solution set for the inequality is the interval .

The graph is show in Fig. 12.

 

 

With no further computations we can deduce the solutions for the desired original equality are the endpoints   and  .

The solution set for   is  .

The graph is shown in Fig. 13.

As a bonus we also know the solution set for the “greater than” inequality is everything else and is therefore   .

The graph is shown in Fig. 14.

 

 


Again it is instructive to graph all three solution sets on the same number line to obtain Fig. 15 and observe that the solution sets do not overlap and their union is the entire real number line.

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