How To Teach Math - Solve Combined Linear Inequalities

A1.2.5 Solve combined linear inequalities

Resources

Compound Inequality Introduction - A worksheet to use with the introduction described below

Compound Inequality Practice - 8 practice problems on compound inequalities

Topic Discussion

I usually introduce combined inequalities in a similar way to regular inequalities. I start with a discussion on the difference between "and" and "or". Then I have the students test points for both kinds of inequalities and plot them. Usually I have students place an "x" for a false point and an enclosed circle for a true point. Then I extend it to help them understand how to solve the problems algebraically.

And versus Or

In order to help students understand how to handle and versus or inequalities I try to incorporate some real world examples. Such as:

"The sky is blue and the grass is green"

"Barrack Obama is running for president and he is 8 feet tall"

"The USA has 48 states or is in North America"

The key to creating these statements is that both must be easily provable facts. Sometimes I will joke with my students and say "IU is the best basketball team and Purdue is terrible", but for the purpose of the lesson the statements can not include opinion. Once I have introduced the statements I work to have the students discussing if they are true. This should then lead to some easy rules about when "and" inequalities and "or" inequalities are true.

Testing Points

As I mentioned above I approach this like the regular inequalities. Except, it is important to be very careful on the points that you pick for the students. But in general that same principals apply. The goal is to get the students thinking what makes the inequalities true and what doesn't. Also they need to be considering what the different graphs look like. The ultimate goal is for them to discover this themselves, but it is also important to formalize it later on.