# Complex Inequality

Pronunciation: /kəmˈplɛks ˌɪn.ɪˈkwɒl.ɪ.ti/ Explain

 Click on the points on the sliders and drag them to change the figure. Why is there nothing showing on the numberline when the red slider shows a number greater than the blue slider? 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

StepEquation(s)DescriptionGraph
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 left-hand side of the inequality states that a member of the inequality must be greater than -2.
5 -2 < a ≤ 3 The right-hand 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

1. McAdams, David E.. All Math Words Dictionary, complex inequality. 2nd Classroom edition 20150108-4799968. pg 39. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. inequality. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/inequality. Buy the book
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 248-253. 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

• 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.

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.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)