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?
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.
