My primary recommendation is that we always simultaneously consider an equation and its two inequality siblings as a group and that we graph all three on the same number line. Law of Trichotomy Applied to Polynomial Inequalities in One Variable: Rule: The procedures demonstrated in Example 1 and Example 2 (of previous two posts) may

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# The Law of Trichotomy – Solution Sets

Law of Trichotomy: If a and b are real numbers, then one and only one of the following is true: a < b a = b a > b The most common arrangement of topics in early algebra courses separates the discussion of solution sets of inequalities from the discussion of solution sets of equations.