Lesson 13: Reintroducing Inequalities

Reintroducing Inequalities

What Is Different?

5 min

Problem

List some values for $x$ that would make the inequality $\text-2x > 10$ true.
What is different about the values of $x$ that make $\text-2x \geq 10$ true, compared to $\text-2x > 10$ ?

Answer

Sample responses: -6, -7, -100, -5.001 (any number less than -5)
Sample response: When $x$ is -5, the inequality $\text-2x \geq 10$ is true, but the inequality $\text-2x > 10$ is false.

Sample Response

Sample responses: -6, -7, -100, -5.001 (any number less than -5)
Sample response: When $x$ is -5, the inequality $\text-2x \geq 10$ is true, but the inequality $\text-2x > 10$ is false.

Anticipated Misconceptions

Students may divide both sides of the inequality by -2 to arrive at the incorrect solution $x>\text-5$ .

Responding to Student Thinking

More Chancesmore_chances

Response: Students will have more opportunities to understand the mathematical ideas addressed here. There is no need to slow down or add additional work to the next lessons.

Standards

Addressing

7.EE.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.B.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.