Inequality Explorers: Testing Solutions to See What Fits!

Mathematics Grades 7th Grade 5:09 Video
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Lesson Description

Explore inequalities and learn how to determine if a number is a solution by testing it in the inequality. This lesson uses real-world examples and interactive exercises to make understanding inequalities fun and engaging!

Video Resource

How to test solutions to inequalities | 6th grade | Khan Academy

Khan Academy

Duration: 5:09
Watch on YouTube

Key Concepts

  • Inequalities use symbols like <, >, ≤, and ≥ to compare values.
  • A solution to an inequality is a value that makes the inequality true.
  • To test a potential solution, substitute the value for the variable in the inequality and simplify.

Learning Objectives

  • Students will be able to define what an inequality is and its components.
  • Students will be able to determine whether a given number is a solution to a specific inequality by substitution.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the meaning of inequality symbols (<, >, ≤, ≥) and what they represent. Briefly discuss the difference between equations and inequalities.
  • Video Viewing (10 mins)
    Watch the Khan Academy video 'How to test solutions to inequalities' (https://www.youtube.com/watch?v=Yh4TXMVq9eg). Encourage students to take notes on the examples provided.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video as a class. Emphasize the steps involved: substitution and simplification. For example: 'Is 3 a solution to x + 5 > 7?'
  • Independent Practice (15 mins)
    Provide students with a worksheet containing various inequalities and potential solutions to test. Encourage students to work individually or in pairs.
  • Wrap-up & Discussion (5 mins)
    Review the answers to the independent practice problems. Address any questions or misconceptions. Briefly introduce the concept that inequalities can have multiple or infinite solutions.

Interactive Exercises

  • Inequality Sort
    Create a set of cards with inequalities and potential solutions. Students sort the cards into two piles: 'Solution' and 'Not a Solution'.

Discussion Questions

  • What does it mean for a number to 'satisfy' an inequality?
  • Can an inequality have more than one solution? Why or why not?
  • How is testing a solution to an inequality similar to solving an equation?

Skills Developed

  • Substitution
  • Simplification
  • Logical reasoning
  • Problem-solving

Multiple Choice Questions

Question 1:

Which of the following symbols represents 'greater than or equal to'?

Correct Answer: ≥

Question 2:

Is x = 4 a solution to the inequality x + 2 < 7?

Correct Answer: Yes

Question 3:

Which number is a solution to the inequality 2x > 10?

Correct Answer: 6

Question 4:

If you substitute a value for x in an inequality and the statement is false, what does that mean?

Correct Answer: The value is not a solution.

Question 5:

Which of the following inequalities is true when x = 1?

Correct Answer: x - 1 ≥ 0

Question 6:

What is the first step in determining if a number is a solution to an inequality?

Correct Answer: Substitute the number for the variable

Question 7:

Is x = 2 a solution to the inequality 3x + 1 ≤ 7?

Correct Answer: Yes

Question 8:

Which inequality uses a 'strict' inequality symbol (meaning the solution cannot be equal to the value)?

Correct Answer: x > 5

Question 9:

Which number satisfies the inequality x - 4 > 0?

Correct Answer: 5

Question 10:

In the inequality x + 2 ≤ 5, which of these values for x are solutions?

Correct Answer: x = 4

Fill in the Blank Questions

Question 1:

The symbol '<' means ___________ than.

Correct Answer: less

Question 2:

A value that makes an inequality true is called a ___________.

Correct Answer: solution

Question 3:

To test if x = 3 is a solution to x + 1 > 4, you must ___________ 3 for x.

Correct Answer: substitute

Question 4:

The inequality symbol '≥' means greater than or ___________ to.

Correct Answer: equal

Question 5:

If 5x < 20, then x must be ___________ than 4.

Correct Answer: less

Question 6:

If a number does not make an inequality true, it is ______ a solution.

Correct Answer: not

Question 7:

The symbols <, >, ≤, and ≥ are all examples of ___________ symbols.

Correct Answer: inequality

Question 8:

In the inequality 2x + 3 < 9, if x = 2, then 2x + 3 equals ___________.

Correct Answer: 7

Question 9:

An inequality can have more than one __________.

Correct Answer: solution

Question 10:

When you substitute a value into an inequality, you need to use the correct order of __________.

Correct Answer: operations

Educational Standards

7.A.3:Represent mathematical situations using equations and inequalities involving variables and rational numbers. 7.A.4:Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.

Teaching Materials

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