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