Solving Absolute Value and Compound Inequalities

[Sarah Stevens]

We have looked at the standards, the Algebra progression, and the 6-8 Equations and Expressions for guidance on solving inequalities. 7.EE4b states that students should solve problems of the form px+q>r and px+q<r. The progression points out that this includes less than or equal to. Does it also include compound inequalities or absolute value inequalities? The HS standards have students graph absolute value equations and systems of inequalities but we can’t identify when they learn to solve compound or absolute value inequalities in one variable. Any guidance would be helpful. Thanks

[lhwalker]

Cathy Kessel did a great job answering this question in HS Algebra > Absolute Value Equations

[Bill McCallum]

Here’s the link that I think Lane is referring to:

http://commoncoretools.me/forums/topic/absolute-value-equations/#post-1799

But I noticed that this is mostly about absolute value equations, not inequalities. I would also point out

7.NS.1.c. … Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

It seems to me that this is the key understanding, and could be applied in many contexts, including inequalities. I’m not sure that breaking this down into discrete activities such as solving absolute value inequalities is helpful.

As for compound inequalities, I see that as a notational device which is within the scope of the standards but which does not rise to the level of an explicit mention (but maybe I am misunderstanding the question here).

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