Equations and Inequalities

Lesson 8

Objective

Define and identify solutions to inequalities.

Common Core Standards

Core Standards

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  • 6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

  • 6.EE.B.8 — Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Foundational Standards

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  • 6.EE.A.1

  • 6.EE.A.2

  • 6.NS.C.7

Criteria for Success

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  1. Define a solution to an inequality as the values for the variable that, when substituted in, make the inequality a true statement.
  2. Use substitution to determine if a given value for a variable is a solution to an inequality.
  3. Understand that there are an infinite number of different solutions to an inequality, compared to an equation.  

Tips for Teachers

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Lessons 8–11 address one-variable inequalities. Students have prior experience reading and interpreting inequality comparisons from Unit 4 when they compared rational numbers. 

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Anchor Problems

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Problem 1

An inequality and an equation are shown below.

$${8x=32}$$           $${8x>32}$$

Which value in the set of numbers {4, 4½, 5} is a solution to the equation?

Which values in the set of numbers {4, 4½, 5} are a solution to the inequality?

Guiding Questions

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Problem 2

In which set of numbers are all of the values solutions to the inequality $${ 1.3x-2<7}$$?

  1.   {0, 3, 7}
  2.   {2, 4, 6}
  3.   {3, 6, 10}
  4.   {8, 10, 12}

Guiding Questions

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Problem 3

Isabel is moving her office to a new location. She has a box that can hold up to 40 pounds, and she has already put 18 ½ pounds in the box. Isabel has several books that each weigh 3 pounds that she also wants to put in the box. 

The inequality $${3x+18{1\over2}≤40}$$, where $$x$$ represents the number of books, can be used to determine how many books Isabel can put in the box without it breaking. 

Which of the following number of books can Isabel put in the box without it breaking? Select all that apply.

  1.   5
  2.   7
  3.   8
  4.   10
  5.   15

Guiding Questions

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Problem Set

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

  • Challenge: Explore absolute value inequalitites. Find at least 5 solutions for $$x$$ and plot them on a number line. $$|x|<4$$ 
    What do you think the graph looks like? 

Target Task

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Problem 1

Which of the following values are solutions to the inequality $${ 5x-8≥42}$$ ? Select all that apply.

  1.   4
  2.   8
  3.   10
  4.   12
  5.   20

Problem 2

How is the inequality $${5x-8≥42}$$ different from the equation $${5x-8=42}$$

Mastery Response

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