Complex Inequality
Pronunciation: /kəmˈplɛks ˌɪn.ɪˈkwɒl.ɪ.ti/ Explain
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 Manipulative 1  Complex Inequality Created with GeoGebra. 

A complex inequality is two or more
inequalities
in a single statement. A complex inequality is a
conjunction
of two or more inequalities. This means that all the inequalities must be
true at the same time. The complex inequality
2 < a ≤ 4 can
also be written 2 < a and
a ≤ 4.

How to Graph a Complex Inequality
Step  Equation(s)  Description  Graph 
1 
2 < a ≤ 3 
This is the inequality to graph 

2 
2 < a ≤ 3 
Since 2 < a, 2 is not included in the inequality. Put a hollow dot at 2. 

3 
2 < a ≤ 3 
Since a ≤ 3, 3 is included in the inequality. Put a solid dot at 3. 

4 
2 < a ≤ 3 
The lefthand side of the inequality states that a member of the inequality must be greater than 2. 

5 
2 < a ≤ 3 
The righthand side of the inequality states that a member of the inequality must be less than or equal to 3. 

6 
2 < a ≤ 3 
Any point that is included in the inequality must be in both rays, so draw a line segment for the points included in both rays. 

7 
2 < a ≤ 3 
Remove the extra rays. 

References
 McAdams, David E.. All Math Words Dictionary, complex inequality. 2nd Classroom edition 201501084799968. pg 39. Life is a Story Problem LLC. January 8, 2015. Buy the book
 inequality. merriamwebster.com. Encyclopedia Britannica. MerriamWebster. Last Accessed 6/25/2018. http://www.merriamwebster.com/dictionary/inequality. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 248253. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n265/mode/1up/search/inequality. Buy the book
More Information
 McAdams, David E.. Inequality. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/i/inequality.html.
Cite this article as:
McAdams, David E. Complex Inequality. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexinequality.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
1/18/2010: Changed figure to GeoGebra application. (
McAdams, David E.)
10/26/2009: Added additional description and 'Graphing Complex Inequalities'. (
McAdams, David E.)
11/28/2008: Initial version. (
McAdams, David E.)