Compound Inequalities

Learn and apply compound inequalities using equations, examples, and interpretation.

Lesson 2 of 53 parts Practice Flashcards

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Intersection with And

Objective: Explain and use intersection with and in an Algebra 1 problem.

An and statement requires both inequalities at once; its solution is the overlap of their solution sets. Only shared points belong.

Worked examples

Try itExample 1.1: Which x satisfies 3<x<7?Show answer

5. Check both strict bounds; the chosen number lies between them. The answer is 5.

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Objective: Explain and use intersection with and in an Algebra 1 problem.

An and statement requires both inequalities at once; its solution is the overlap of their solution sets. Only shared points belong.

Worked examples

Try itExample 1.1: Which x satisfies 3<x<7?Show answer

5. Check both strict bounds; the chosen number lies between them. The answer is 5.

Objective: Explain and use union with or in an Algebra 1 problem.

An or statement accepts values satisfying either inequality; its solution is the union of both sets. Yes, when the conditions point outward.

Worked examples

Try itExample 2.1: Which x satisfies 6<x<10?Show answer

8. Check both strict bounds; the chosen number lies between them. The answer is 8.

Objective: Explain and use interval notation in an Algebra 1 problem.

Parentheses exclude endpoints and square brackets include them, while infinity always uses parentheses. It is not a finite real number in the set.

Worked examples

Try itExample 3.1: Which x satisfies 9<x<13?Show answer

11. Check both strict bounds; the chosen number lies between them. The answer is 11.

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