Download Notes on Compound Inequalities keynote

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
4x – 9 = 0 or 3x + 5 = 2
X – 6 = 1 and x + 2 = 9
2w – 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.