Unit 2 – Week 5Reasoning with Linear Equations and

Inequalities

Lesson 2

Students will work with inequality equations and learn why you reverse the inequality sign when you multiply or divide both sides by a negative

number.

Standards

• A.CED.1 – Create inequalities in one variable and use them to solve problems. (integer inputs only)

• A.CED.3 – Represent constraints by inequalities and interpret data points as possible or not possible solutions.

• A.REI.3 – Solve linear equations in one variable including equations with coefficients represented by letters.

Essential Questions

• How are linear equations and Inequality equations similar and different?

• When we apply the Commutative, Associative or Distributive properties to rewrite an inequality does the solution set change?

Read, Write, Draw, Solve

• Given 2x + ax – 7 > -12, determine the largest integer value of a when x = -1.

Activator

• Solve each equation below. Show the solutions set in words, set notation, and graphically.

A. 5x – 7 = 3B. 5x – 7 > 3

Are the solutions the same for both equations? Why or why not?

Solve each inequality below.

A. 5x – 7 > 3

B. -5x – 7 > 3

Let’s check our answers! What if x = 3, will the inequalities be true?

Solve each inequality below.

A. 2x > 8

B. 2x > -8

C. -2x > 8

Let’s check our answers! What if x = 5, will the inequalities be true?

Solve each inequality below.

A.

B.

C.

Let’s check our answers! What if x = 5, will the inequalities be true?

Solve each inequality below.

A. x + 3 ≤ 5

B. -x + 3 ≤ 5

Let’s check our answers! What if x = -2, will the inequalities be true?

Practice

Summarizer

Fergus was absent for today’s lesson and asked Mike to explain why the solution to is . Mike said, “Oh! That’s easy. When you multiply by a negative, just flip the inequality.” Provide a better explanation to Fergus about why the direction of the inequality is reversed.