basic mathematics image
 basic mathematics image

Compound inequality


A compound inequality is a statement in which two inequalities are connected by the word "and" or the word "or".

For example, x > 5 and x ≤ 7         and        x ≤ -1 or x > 7 are examples of compound inequalities

When the word that connects both inequalities is "and", the solution is any number that makes both inequalities true

When the word that connects both inequalities is "or", the solution is any number that makes either inequalities true

For example, graph the following compound inequality: x ≥ 2 and x < 4

The graphs for x ≥ 2 and x < 4 should look like this:


numberline-image

Putting the two graphs together gives the following:


numberline-image

The solution is that portion of the graph where you see red and blue at the same time( Or the portion shaded twice)

If you pull this out from the graph above, we get:


numberline-image

This means that the solution is any number between 2 and 4, to include 2, but not 4.

Notice that the open circle (in red) means that 4 is not included

Graph x ≥ - 2 and x > 1

The graphs for x ≥ - 2 and x > 1 should look like this:


numberline-image

Putting the two graphs together gives the following:


numberline-image

The solution is that portion of the graph where you see red and blue at the same time( Or the portion shaded twice)

If you pull this out from the graph above, we get:


numberline-image

The solution is any number after 1

However, if we twist the same problem above and graph x ≥ - 2 or x >, it is a different story

Since the "or" means either, the solution will be the shaded area that include both inequalities.

The solution is thus any number after -2

numberline-image


Graph x > 2 or x < -3


Here it is!

numberline-image

However, if for the same problem right above, I replace "or" by "and", there will be no solutions for this compoud

Look carefully again at the graph right above and you will see that blue and red don't meet. That is why they have nothing in common and thus no solutions







Page copy protected against web site content infringement by Copyscape





worksheets-banner










Copyright © 2008-2015. Basic-mathematics.com. All right reserved

Are you a fan of this site? Support us     Our awards!     Our partners     About me     Disclaimer     Build your website!     Advertise on my site
    Try our free toolbar     Like us on Facebook     Take our survey     Illustrated fractions     Educational math software     Math jobs     Best Teacher Sites Now     Teachers/Students tools     Search math jobs     Algebra ebook     Fraction ebook     Geometric formulas ebook