Curriculum  /  Math  /  9th Grade  /  Unit 3: Linear Expressions & Single-Variable Equations/Inequalities  /  Lesson 11

Linear Expressions & Single-Variable Equations/Inequalities

Lesson 11

Math

Unit 3

9th Grade

Lesson 11 of 12

Objective

Write and graph compound single-variable inequalities to describe the solution to contextual and non-contextual situations.

Common Core Standards

Core Standards

  • A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

  • 7.EE.B.4.B

Criteria for Success

  1. Write an inequality that has both a minimum and a maximum value from a contextual situation. Identify this as a compound inequality. 
  2. Solve compound inequalities and identify the solutions as either inclusive, exclusive, or either a union or disjoint. 
  3. Use appropriate notation to algebraically write a compound OR inequality and appropriate notation to algebraically write a compound AND inequality (inclusive and exclusive). 
  4. Use appropriate notation to graphically show the solution set of a compound inequality (inclusive, exclusive, and, or).
  5. Identify when an inequality is used inappropriately in either mathematical or contextual situations. 
  6. Describe why a compound inequality is necessary in contextual situations, and use $${x > 0}$$ and $${y > 0}$$ to denote positive solutions for a context.
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Anchor Problems

25-30 minutes

Problem 1

At Sea World, kids are only allowed into the Air Bounce if they are between 37 and 61 inches tall. They are only allowed on the Tide Pool Climb if they are 39 inches tall or under. 

  1. Show the allowable heights for the rides on separate number line, and represent each with inequalities. 

Air Bounce:


Tide Pool Climb: 

  1. Using inequalities and a number line, describe the height of kids who can go on both the Air Bounce and the Tide Pool Climb.

Guiding Questions

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References

Illustrative Mathematics Height Requirements

Height Requirements, accessed on Sept. 14, 2017, 2:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

Which inequality in each row is valid? Draw a number line below the description to help explain your reasoning.

A number is greater than 10 and less than 5.  A number is greater than 5 and less than 10.
A number is less than 8 or greater than 4.  A number is less than 4 or greater than 8.
$${2<x>5}$$ $${2<x<5}$$
$${x<7}$$ or $${x>9}$$ $${x<9}$$ or $${x>7}$$
  • For the true inequalities written in words, write the inequality algebraically. 
  • For the true inequalities written algebraically, write the inequality in words.

Guiding Questions

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Problem 1

Which one of these inequalities is valid? Explain your reasoning using a number line and in words.

 

Inequality 1:    $${-1\leq x\leq 1}$$

 

Inequality 2:    $${x\leq1}$$ or $${x\geq -1}$$

References

EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 15 — Exit Ticket

Algebra I > Module 1 > Topic C > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Write the inequalities shown in the graphs below. 

 

Inequality 1: 

 

Inequality 2:

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students write a single inequality to represent the solution set of $${x>4 }$$ or $${x>6}$$. Describe how this is not a compound inequality. 
  • Include problems where students need to graph inclusive and exclusive, bounded and unbounded inequalities written algebraically and in word form. 
  • Include problems where students need to describe a compound inequality from a graph both algebraically and in word form. 
  • Include problems where students distinguish the solution set of an equation graphed from the solution set of an inequality graphed. 
  • Include error analysis problems where students identify a solution that is not in the solution set of a compound inequality. Use graphical and algebraic analysis to show that this student is not correct.

Next

Solve and graph compound inequalities where algebraic manipulation is necessary in contextual and non-contextual situations.

Lesson 12
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations

Topic B: Modeling with Single-Variable Linear Equations

Topic C: Properties and Solutions of Single-Variable Linear Inequalities

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