Compound inequality

Definition

A compound inequality consists of two or more inequalities joined by 'and' or 'or'. It describes a range of values that satisfy either both conditions (for 'and') or at least one condition (for 'or').

5 Must Know Facts For Your Next Test

1. A compound inequality using 'and' is only true if both inequalities are true.
2. A compound inequality using 'or' is true if at least one of the inequalities is true.
3. To solve a compound inequality, treat each part separately before combining results.
4. The solution to an 'and' compound inequality is typically represented as an intersection of two sets on a number line.
5. The solution to an 'or' compound inequality is typically represented as the union of two sets on a number line.

Review Questions

• Solve and graph the compound inequality $3 < x + 2 \leq 7$.
• What does it mean when we say a compound inequality uses 'or'?
• How do you represent the solution of an 'and' compound inequality on a number line?

Related terms

Linear Inequality:

An algebraic expression where one side is not equal to the other, typically involving variables raised to the first power.

Absolute Value Inequality:

An inequality that involves the absolute value function, which measures distance from zero.

Intersection:

The set containing all elements that are common to both sets, often used in solving 'and' compound inequalities.