Compound Inequality

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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="">
  • 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="">

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="" ≥="">
    C. x < -7="" o="" 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.

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