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.

Video Examples: Compound Inequalities


Solved Example onCompound Inequality

Ques: 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.