Equations and Inequalities

Lesson 11

Objective

Solve word problems leading to inequalities in the forms $${px+q>r}$$  or $${px+q<r}$$  and $${p(x+q)>r}$$ or $${p(x+q)<r}$$.

Common Core Standards

Core Standards

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  • 7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Foundational Standards

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  • 6.EE.B.5

  • 6.EE.B.8

Criteria for Success

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  1. Write inequalities to represent real-world situations. 
  2. Solve inequalities and interpret solutions in context.

Tips for Teachers

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Continue to include procedural practice problems solving equations and inequalities without context.

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Anchor Problems

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Problem 1

A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 525 cars on the lot, and the general manager estimates that they will consistently sell 50 cars per week. Estimate how many weeks it will take for the number of cars on the lot to be fewer than 75.

  1. Write an inequality that can be used to find the number of full weeks, $$w$$, it will take for the number of cars to be fewer than 75. Since w is the number of full or complete weeks,$$ w=1$$ means at the end of week 1. 
  2. Solve and graph the inequality.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic B > Lesson 15Example

Grade 7 Mathematics > Module 3 > Topic B > 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

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can only carry 1,200 pounds of people and gear for safety reasons. Assume the average weight of a person is 150 pounds. Each group will require 200 pounds of gear for the boat plus 10 pounds of gear for each person.

  1. Create an inequality describing the restrictions on the number of people possible in a rented boat. Graph the solution set.
  2. Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5 people. Group 3 has 8 people. Which of the groups, if any, can safely rent a boat? What is the maximum number of people that may rent a boat?

Guiding Questions

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References

Illustrative Mathematics Fishing Adventures 2

Fishing Adventures 2, accessed on Nov. 9, 2017, 5:22 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 Set

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Target Task

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The members of a singing group agree to buy at least 250 tickets for an outside concert. The group buys 20 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought? 

Write and solve an inequality. Explain your answer in context of the situation. 

References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic B > Lesson 15Exercise 4

Grade 7 Mathematics > Module 3 > Topic B > 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..

Modified by The Match Foundation, Inc.

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