This activity is intended to supplement Algebra I, Chapter 6, Lesson 3.
Time required: 60 minutes
In this activity, students first look at tables of values to see that inequalities (in a single variable) are true for some values of the variable and not for others. They are guided to connect “true” with a value of 1 and “false” with a value of 0, creating a bridge from the table of values to a graph of the linear inequality. In Problem 2, students solve one-step linear inequalities using addition or subtraction and compare the graph of the original inequality with that of the simplified form, finding they are the same. In Problem 3, students perform a similar exploration solving one step linear inequalities using multiplication or division.
Topic: Linear Inequalities
Graph a simple linear inequality of the form x<a, x≤a, x>a, or x≥a on the real line.
Use addition or subtraction to solve a “one step” linear inequality in a single variable.
Use multiplication or division to solve a “one step” linear inequality in a single variable.
Teacher Preparation and Notes
This activity is designed for use in an Algebra 1 or Pre–Algebra classroom.
Prior to beginning the activity, students should download the LINEQUA program to their calculators. They should also have some experience solving simple one-step and multiple-step linear equations.
This activity is intended to be a combination of teacher-led and student-centered activity. It is recommended that you introduce each problem by guiding students through the step-by-step instruction in a whole-class setting, and then allow them to complete the exercises individually or in small groups with your assistance.
If time constraints prevent you from completing the activity in one class period, you may choose to complete Problem 1 one day and Problems 2 and 3 the next day.
To download the calculator program, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=8773 and select "LINEQUA.8xp".
Solving inequalities in a single variable is similar to solving equations in a single variable, but there are some important differences. One big difference occurs when you multiply or divide by a negative number. In this activity, you will practice solving linear inequalities and explore these differences using algebraic and graphing techniques.
Problem 1 – Table of Values
Problem 2 – Graphing
The following examples show how to sketch the graph of an inequality on paper. Explain the two inequalities to students before doing the exercises.
Problem 3 – Solving inequalities using addition and subtraction
Students will compare the starting inequality and the final inequality using the Compare Ineq choice in the LINEQUA program. The first inequality entered will appear in the top half of the screen. The second inequality entered will appear in the bottom half of the screen.
Caution: In some graphs, the open circle will appear to be filled in. This is because of the size of the pixels on the graph screen. For this reason, a “closed circle” is shown as a cross, and an “open circle” as a dot.
Problem 4 – Solving inequalities using mulitplication and division
Students are to graph four different pairs of inequalities that involve multiplication or division. This will lead them an investigation of when the inequality symbol is flipped or reversed.
15. a) yes; they have the same solutions
16. a) yes; they have the same solutions
17. a) no; they do not have the same solutions
18. a) yes; they have the same solutions