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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