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Published byOpal Webb Modified over 9 years ago

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A compound statement is made up of more than one equation or inequality. A disjunction is a compound statement that uses the word or. Disjunction: x ≤ –3 OR x > 2 Set builder notation: {x|x ≤ –3 U x > 2} A disjunction is true if and only if at least one of its parts is true. A conjunction is a compound statement that uses the word and. Conjunction: x ≥ –3 AND x < 2 Set builder notation: {x|x ≥ –3 x < 2}. A conjunction is true if and only if all of its parts are true. Conjunctions can be written as a single statement as shown. x ≥ –3 and x< 2 –3 ≤ x < 2 U

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Example 1A: Solving Compound Inequalities Solve the compound inequality. Then graph the solution set. Solve both inequalities for y. The solution set is all points that satisfy {y|y < –4 or y ≥ –2}. 6y < –24 OR y +5 ≥ 3 6y < –24y + 5 ≥3 y < –4y ≥ –2 or –6 –5 –4 –3 –2 –1 0 1 2 3 (–∞, –4) U [–2, ∞)

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Solve both inequalities for c. The solution set is the set of points that satisfy both c ≥ –4 and c < 0. c ≥ –4c < 0 –6 –5 –4 –3 –2 –1 0 1 2 3 [–4, 0) Example 1B: Solving Compound Inequalities Solve the compound inequality. Then graph the solution set. and 2c + 1 < 1

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Example 1C: Solving Compound Inequalities Solve the compound inequality. Then graph the solution set. Solve both inequalities for x. The solution set is the set of all points that satisfy {x|x < 3 or x ≥ 5}. –3 –2 –1 0 1 2 3 4 5 6 x – 5 < –2 OR –2x ≤ –10 x < 3 x ≥ 5 x – 5 < –2 or –2x ≤ –10 (–∞, 3) U [5, ∞)

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