A compound inequality is a mathematical statement consisting of two or more inequalities connected by AND or OR.

A compound inequality containing the word "or" is called a disjunction and is true when EITHER of the inequalities is true.

A compound inequality containing the word "and" is called a conjunction and is true only when BOTH inequalities are true.

Example 1 (Disjunction: x > 2 or x ≥ 5 )

Example 2 (Conjunction: x > 2 and x ≥ 5 )

Example 1 (Disjunction: x > 2 or x ≤ 5 )

Example 2 (Conjunction: x > 2 and x ≤ 5 )

Example 1 (Disjunction: x < 2 or x ≥ 5 )

Note that the compound inequality above ( x < 2 or 5 ≥ x ) cannot be combined into a single statement, as in Examples (Set TWO): Example 2: ( 2 < x and x ≤ 5 ) is equivalet to ( 2 < x ≤ 5 ).

Example 2 (Conjunction: x < 2 and x ≥ 5 )