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In this lesson, we show students how to model linear inequalities (one-step and two-step) on a number line. Students reason with simple inequalities (e.g, a < 2) and inequalities with operations (e.g., 2a + 1 > 5) to identify values for the variable that will make the inequality true, values that will leave the truth value unknown, and values that will make the inequality false. Students generate different solutions for linear inequalities by substitution.
Students complete practice problems using interactive diagrams to model inequalities on a number line and writing the solutions as an inequality. Then students use a similar interactive diagram to model equations on a number line and write the solution as an equation. We are creating the connection here between inequality and equation statements and their solutions.
Module 1 Video
The video shows the basics of modeling inequalities and equations on a number line. You can pause the video and discuss ideas about how to determine the value of x. Although we will present a model that can be used to think about ways to solve some kinds of inequalities, it is not necessary for the purposes of these lessons, to present the method. It is enough here to reason about what x could be. Thinking about this long enough should yield that x must be less than 3.5 for 2x + 3 < 10, and greater than 3.5 for 2x + 3 > 10.