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

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Example: Solve the inequality |3x – 5| > 6. Discussion and Solution:  We begin by focusing not on the given inequality, but on its counterpart |3x – 5| < 6 which we immediately convert to the equivalent compact compound inequality.     The solution set for |3x – 5| < 6 is the interval .

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

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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.