Curriculum  /  Math  /  9th Grade  /  Unit 3: Linear Expressions & Single-Variable Equations/Inequalities  /  Lesson 12

Linear Expressions & Single-Variable Equations/Inequalities

Lesson 12

Math

Unit 3

9th Grade

Lesson 12 of 12

Objective

Solve and graph compound inequalities where algebraic manipulation is necessary in 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.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • 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. Separate compound "and" inequalities into two inequalities to add validity to the mechanics of solving a compound "and" inequality. 
  2. Use the mechanics of solving a compound inequality to identify the solution set to compound inequalities. 
  3. Graph compound inequalities and verify solutions through substitution into the original inequalities. 
  4. Write, solve, and graph contextual compound inequalities in need of algebraic manipulation.
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Anchor Problems

25-30 minutes

Problem 1

Part A: 
Describe the solution set to the inequality “$$x$$ is greater than $${-4}$$ and less than $$5$$” algebraically and graphically.

 

Part B: 
Graph the solution set to the compound inequality shown below. 

$$-5<2x+ 1<4$$

Guiding Questions

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Problem 2

Jonah got a 76 on his midterm exam. To get a B in the course, the average of his midterm and his final must be between 80 and 89. 

Write and solve a compound inequality that models this context. Describe the solution set in context of the problem.

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

Solve each compound inequality for $$x$$ and graph the solution on a number line. 

 

a.    $${9+2x<17}$$ or $${7-4x<-9}$$

 

b.    $${6\leq \frac{x}{2}\leq11}$$

 

References

EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 16 — Exit Ticket

Algebra I > Module 1 > Topic C > Lesson 16 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

Jason is shopping for his first car. He wants to spend a total of no more than $18,000 but knows he needs to spend at least $10,000 to get a decent car. He also knows there is a 6% sales tax, and he’ll need to pay fees of $150 to get the car registered and inspected. What is the range of prices Jason should be looking at to keep him within budget? 

Write and solve a compound inequality that describes this situation. Graph the solution, and describe the solution in the context of the problem.

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 are given the solution to a compound inequality and they need to identify possible inequalities from this solution set.
  • Include contextual problems where students need to graph the solution set and describe the solution in the context of the problem.

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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