1. Unit 2 – Week 5 Reasoning 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.

2. 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.

3. 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?

4. Read, Write, Draw, Solve Given 2x + ax – 7 > -12, determine the largest integer value of a when x = -1.

5. Activator Solve each equation below. Show the solutions set in words, set notation, and graphically. A.5x – 7 = 3 B.5x – 7 > 3 Are the solutions the same for both equations? Why or why not?

6. 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?

7. 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?

8. Solve each inequality below. A. B. C. Let’s check our answers! What if x = 5, will the inequalities be true?

9. 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?

10. Practice

11. 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.