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.

Graphing Complex Inequalities
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
 inequality. merriamwebster.com. Encyclopedia Britannica. MerriamWebster. Last Accessed 8/6/2018. http://www.merriamwebster.com/dictionary/inequality.
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 248253. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. 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. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexinequality.html.
Image Credits
Revision History
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.)