3.2.2 Solving Inequalities with Variables on Both Sides (continued) Example 4 All Real Numbers as Solutions or No Solutions As with equations, there are special cases of inequalities called identities and contradictions. Inequalities that are identities have all real numbers as solutions. Inequalities that are contradictions have no solutions. If using inverse operations to isolate the variable results in a numerical statement that is true, such as 1 < 2, then the inequality is an identity with all real numbers as solutions. If using inverse operations to isolate the variable results in a numerical statement that is false, such as 1 > 2, then the inequality is a contradiction with no solutions.
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