compound inequality


Definition of Compound Inequality

  • Compound Inequality is two or more simple inequalities joined by the terms 'and' or 'or'.

Examples of Compound Inequality

  • 0 ≤ x ≤ 4 is an example of compound inequality, which says that x is either 0 or 4, or any number between 0 and 4.
  • x > 5 and x < 11="" is="" a="" compound ="" inequality,="" which="" says="" that="">x takes values greater than 5 and less than 11.
  • y < -="" 13="" or="">y ≥ 10 is a compound inequality, which says that the values of y are either less than - 13 or greater than or equal to 10.

Solved Example on Compound Inequality

Choose a compound inequality that represents the set of all real numbers less than or equal to - 7 or greater than or equal to 5.
Choices:
A. x ≤ - 7 or x > 5
B. x < -="" 7="" or="">x ≥ 5
C. x < -="" 7="" or="">x > 5
D. x ≤ - 7 or x ≥ 5
Correct Answer: D
Solution:
Step 1: The algebraic model for the statement is x ≤ - 7 or x ≥ 5.
Step 2: The graph of this compound inequality is shown below. Notice that the graph has two parts. One part lies to the left of -7. The other part lies to the right of 5.

Related Terms for Compound Inequality

  • Inequality