Compound Inequalities

A compound inequality is a sentence which consists of two inequality statements joined either by “or” or by “and.”

“And” indicates that both statements of the compound sentence are true at the same time. It is also called the intersection.

Examples of conjunctions:
x > –5 and x < –2
x < 4 and x > –4

“Or” indicates that the entire compound sentence is true as long as either statement is true. It is also called the union.

Examples of disjunctions
x > –5 or x < –2
x < 4 or x > –4

Example:

Use a number line to find the values for the following compound inequalities

a) x > –2 and x < 3

b) x < 2 and x ≤ –1

c) x < –3 and x ≥ 1

Solution:

a) x > –2 and x < 3

Common values: – 2 < x < 3

b) x < 2 and x ≤ –1

Videos

Solving compound inequalities - and, intersection, or, union
Professor Edward Burger explains solving compound inequalities.

More on compound inequalities -
Professor Edward Burger explains more on compound inequalities.

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