Unit 2 Week 5 Reasoning with Linear Equations

Unit 2 – Week 5 Reasoning with Linear Equations and Inequalities Lesson 3 Students describe the solution set of two equations or inequalities joined by either “and” or “or” and graph the solution set on a number line. Lesson 15 Story of Functions

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 • What is a compound sentence? • What is a declarative sentence? • Does the word “and” mean the same thing in a compound mathematical sentence as it does in an English sentence? • What is a compound math sentence?

Read, Write, Draw, Solve • Determine whether each claim given below is true or false. A. B. C. D. E. F. Right now, I am in math class and English class. Right now, I am in math class or English class. 3+5=8 and 5<7 -1. 10+2≠ 12 and 8 -3>0. 3<5+4 or 6+4=9. 16 -20>1 or 5. 5+4. 5=11 • These are all examples of declarative compound sentences. G. H. When the two declarations in the sentences above were separated by “and, ” what had to be true to make the statement true? When the two declarations in the sentences above were separated by “or, ” what had to be true to make the statement true?

Discussion - Activator • How does the word “and” mean the same thing in an English sentence and a math sentence?

Discussion • How does the word “or” mean a similar thing in a compound mathematical sentence as it does in an English sentence?

Let’s look at some A. B. C. D. x + 8 = 3 or x – 6 = 2 4 x – 9 = 0 or 3 x + 5 = 2 X – 6 = 1 and x + 2 = 9 2 w – 8 = 10 and w > 9

Exercise 2 Questions • In order for the compound sentence x > -1 and x < 3 to be true, what has to be true about x? • Where do the solutions lie on the graph? • What are some solutions that are possible for this compound inequality? • How many solutions are there to this compound inequality?

Ways to write you solution set • X can be any number that is between -1 and 3 • -1 < x < 3 • Or displayed on the number line

Exercise 3 Questions • In order for the compound sentence x < -4 or x > 0 to be true, what has to be true about x? • Where do the solutions lie on the graph? • What are some solutions that are possible for this compound inequality? • Would it be acceptable to write this compound sentence as follows: 0 < x < -4? Why or why not? • How many solutions are there to this compound inequality?

Ways to write you solution set • Sentence • Abbreviation • Number Line

Continue with Practice

Summarizer Consider each of the following compound sentence. x < 1 and x > -1 x < 1 or x > -1 Does changing the word from ‘and’ to ‘or’ change the solution set? Explain why. Create a number line graph for each compound sentence to support your reasoning.