In this lesson, students revisit the meaning of the solutions to an inequality in one variable and recall that the solution set is a range of values. They also investigate different ways to find the solution set to an inequality—by reasoning about the quantities and relationships in context, by guessing some values, substituting them into the inequality, and checking them to see if they make an inequality true, and by first solving a related equation in one variable. Along the way, students reason abstractly and quantitatively (MP2).
Two optional activities are included in this lesson. The first is to give students an additional opportunity to make sense of the solutions to an inequality in terms of a situation. The second optional activity introduces them to graphing twovariable equations as a way to find solutions to onevariable inequalities.
Later, students will use the understanding they build here to solve more sophisticated problems and to find solutions to linear inequalities in two variables.
Lesson overview
 19.1 Warmup: Find a Value, Any Value (5 minutes)
 19.2 Activity: Off to an Orchard (20 minutes)
 19.3 Optional Activity: PartTime Work (20 minutes)

19.4 Activity: Equality and Inequality (10 minutes)
 Includes "Are you Ready for More?" extension problem

19.5 Optional Activity: More or Less? (15 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 19.6 Cooldown: Seeking Solutions (5 minutes)
Learning goals:
 Find the solution to a onevariable inequality by reasoning and by solving a related equation and testing values greater than and less than that solution.
 Graph the solution to an inequality as a ray on a number line and interpret the solution in context.
 Understand that the solution to an inequality is a range of values that make the inequality true.
Learning goals (student facing):
 Let’s find and interpret solutions to inequalities in one variable.
Learning targets (student facing):
 I can graph the solution to an inequality in one variable.
 I can solve onevariable inequalities and interpret the solutions in terms of the situation.
 I understand that the solution to an inequality is a range of values (such as \(x>7\)) that make the inequality true.
Required preparation:
 Devices that can run Desmos (recommended) or other graphing technology are needed for the optional activity, More or Less?
 The digital version with an embedded applet is recommended for all classes.
Standards:
 This lesson builds on the standard: CCSS.7.EE.B.4.bMS.7.EE.4bMO.7.EEI.B.4c
 This lesson builds towards the standards: CCSS.HSACED.A.1MS.ACED.1CCSS.HSAREI.B.3MS.AREI.3MO.A1.CED.A.1
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.