1. Representations of Inequalities

2. Table of Contents
41: How Do I Represent Inequalities in Different Ways?
40: Warm-Up, Guided Practice Worksheet

3. Warm Up
What are the four representations of functions and what do they mean?

4. Learning Intention/Success Criteria
LI: We are learning to write inequalities in four representations.
SC: I know how to -represent inequalities in 4 ways: symbolically, visually, set notation, and verbally -recognize and compare slope from a graph -write inequalities describing when one graph is larger than another.

5. EQ: How Do I Write Inequalities in Different Ways?
11/10/2018

6. Inequality
A mathematical sentence built from expressions using one or more of the following symbols:
< > ≤ ≥
Less Than
Greater Than
Less Than or Equal To
Greater Than or Equal To

7. ●
Closed Circle
Used to represent the inequality greater than or equal to OR less than or equal to.
The point is part of the solution ○
Open Circle
Used to represent the inequality greater than OR less than.
The point is NOT part of the solution

8. Four Ways to Represent Inequalities
1. Symbolically
Writing an inequality with inequality signs (<, >, ≥, or ≤)
Also know as symbolic notation
Examples:
x > 3
2 < k ≤ 40
g ≤ 6

9. 2. Visually
Graphing inequalities on a number line or coordinate grid
An open circle with an arrow or a dotted line is used if the inequality is less than OR greater than
A closed circle with an arrow or a solid line is used if the inequality is less than or equal to OR greater than or equal to

10. 3. Set Notation
Writing inequalities with brackets
Written in the form: { variable : symbolic notation }
{ } = brackets; shows this is a set
Variable = the variable you are using
: = “such that”

11. Example: { x : x > 3}
Spoken: the set of all x’s such that x is greater than 3

12. 4. Verbally
Using words to describe the inequality
Example:
x is greater than 3

13. Example 1: Write the inequality in 4 representations of inequalities
Symbolic: Visual: Set: Verbal:
m > 7
{ m : m > 7}
All values m greater than 7

14. Guided Practice
For each row, fill in the missing columns to show different ways of representing the same inequality., Then, in the last column, circle all values that are solutions to the inequality represented in that row.

15. Guided Practice 1a
Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions:
k > 3
All values of k greater than 3
{ k : k > 3 }
9 6 12

16. Guided Practice 1b
Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions:
g ≤ 2
All values g less than or equal to 2
{ g : g ≤ 2 }
-2 ½ -8/

17. Guided Practice 1c
Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions:
d < 2/3
All values d less than 2/3
{ d : d < 2/3 }
-2 ½ -8/

18. Guided Practice 1d
Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions:
x ≥ -1
All values x greater than or equal to -1
{ x : x ≥ -1 }
9 ½

19. Example 2: Use the graph of the linear functions to answer questions

20. Which is greater, f(2) or g(2)? How do you know?
f(2) is greater than g(2).
I know this because f(2) = 3 and g(2) = 1. Since 3 is bigger than 1, f(2) is greater.
For which value of x is f(x) = g(x)?
f(x) is equal to g(x) when x = 1.

21. For which values of x is f(x) ≥ g(x)? Write your answer in set notation.
{ x : x ≥ 1 }
For which values of x is f(x) < g(x)? Write your answer in set notation.
{ x : x < 1 }

22. Guided Practice 2
a) Is f(-4) < g(-4)? Explain how you can tell b) For which values of x is it true that f(x) ≤ g(x)? Write your answer in set notation c) For which values of x is it true that f(x) ≥ g(x)? Show the solution on a number line.

23. Guided Practice 2 Answers
a) g(-4) is larger than f(-4). You can tell by inferencing how the linear graphs would continue
b) { x : x ≤ -3 } c) -3