Complex Inequality

Pronunciation: /kəmˈplɛks ˌɪn ɪˈkwɒl ɪ ti/ ?

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Manipulative 1: Complex Inequality. Click on the points and the blue and red sliders and drag them to change the figure. Double click on the figure to open it in a separate window.

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

StepEquation(s)DescriptionGraph
1-2 < a ≤ 3This is the inequality to graphNumber line from -3 to 3.
2-2 < a ≤ 3Since -2 < a, -2 is not included in the inequality. Put a hollow dot at -2.Number line from -3 to 3 with a hollow dot at -2.
3-2 < a ≤ 3Since a ≤ 3, 3 is included in the inequality. Put a solid dot at 3.Number line from -3 to 3 with a hollow dot at -2 and a solid dot at 3.
4-2 < a ≤ 3The left-hand side of the inequality states that a member of the inequality must be greater than -2.Number line from -3 to 3 with a hollow dot at -2 and a solid dot at 3. A ray extends from -2 in the positive direction.
5-2 < a ≤ 3The right-hand side of the inequality states that a member of the inequality must be less than or equal to 3.Number line from -3 to 3 with a hollow dot at -2 and a solid dot at 3. A ray extends from -2 in the positive direction. A ray extends from 3 in the negative direction.
6-2 < a ≤ 3Any point that is included in the inequality must be in both rays, so draw a line segment for the points included in both rays.Number line from -3 to 3 with a hollow dot at -2 and a solid dot at 3. A ray extends from -2 in the positive direction. A ray extends from 3 in the negative direction. A line segment extends from -2 to 3.
7-2 < a ≤ 3Remove the extra rays.Number line from -3 to 3 with a hollow dot at -2 and a solid dot at 3. A line segment extends from -2 to 3.

References

  1. inequality. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-18). http://www.merriam-webster.com/dictionary/inequality.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 248-253. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n265/mode/1up/search/inequality.

More Information

  • McAdams, David. Inequality. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-10-26. http://www.allmathwords.org/article.aspx?lang=en&id=Inequality.

Cite this article as:


Complex Inequality. 2010-01-18. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexinequality.html.

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Revision History


2010-01-18: Changed figure to GeoGebra application. (McAdams, David.)
2009-10-26: Added additional description and 'Graphing Complex Inequalities'. (McAdams, David.)
2008-11-28: Initial version (McAdams, David.)

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