Download Representing Inequalities Inequalities Recall: Word Expression

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Representing Inequalities
Inequalities
Recall:
Word Expression
a is less than b
a is greater than b
a is at least b
a is no less than b
a is at most b
a is no more than b
Interpretation
a<b
a>b
a≥b
a≥b
a≤b
a≤b
When you solve an inequality you have multiple solutions
Because it’s impossible to list all the solutions, we can represent the answer using a few
different forms:




An inequality statement
A graph on a number line
Interval Notation
Set Builder Notation
Graphing an Inequality on a Number Line
When you just want greater than or less than, you use an
on the graph.
When you want (greater than or equal to) or (less than or equal to), you’ll use
Examples:
1.
x3
2.
x  2
3.
1  x  4
Interval notation is another method for writing inequalities. Keep these things in mind:
Open Parenthesis: ( )
Closed Parenthesis: [ ]
Infinity: ∞
Negative Infinity: - ∞
Union:
Used if the value is not included in the inequality.
Used if the value is included in the inequality.
The upper end of the inequality goes on forever in the
positive direction.
The lower end of the inequality goes on forever in the
negative direction.
Used to join two intervals together when there is a break
in the graph
So…When using Interval Notation we will be using:
 Square brackets [ ] to include the endpoint.
 Parenthesis to ( ) to exclude the endpoint.
Examples:
4.
x3
5.
x  2
6.
1  x  4
Set-builder notation is mathematical shorthand for precisely stating all numbers of a
specific set that possess a specific property.
x 2  x  6
" x are the elements of the set of real numbers, such
that, x is between 2 and 6 not including 2”
Examples:
7.
x3
8.
x  2
9.
1  x  4
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Practice!
Verbal Phrase
1.
All real numbers less than 2
2.
All real numbers greater
than −2
3.
All real numbers less than or
equal to 1
4.
All real numbers greater
than or equal to 0
5.
All numbers great then 1 and
less than or equal to 5
6.
All number that are either
less then -2 or greater then 3
7.
All real numbers
Inequality
Graph
Interval
Notation
Set Notation
Try It on Your Own!
Fill in the Missing Pieces of the Chart!
Verbal Phrase
Inequality
8.
Ex.
All numbers greater than
or equal to 1 and less than
4.
Graph
1 x  4
Interval
Notation
[1,4)
Set Notation
x 1  x  4
9.
The numbers between -3
and 3 not including either.
10.
11.
( , 4)
  x  
12.
13.
[5, )
x  1 or x  5
14.
-4 -3 -2-1 0 1 2 3 4 5
15.
x x  2 or x  3
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Homework: Interval and Set Notation
Use interval notation to describe the number(s) graphed on each number line.
1.
2.
3.
-6
-4
-2
0
2
4
6
-6
4.
-4
-2
0
2
4
6
5.
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
6.
-6
-4
-2
0
2
4
6
Describe the intervals using interval notation.
Union: the symbol 
7.
Numbers that…
• belong in one set OR another
• are brought together
We could describe the numbers that belong to the
interval (-5, -1] OR the interval (2, 4) through
the notation (-5, -1]  (2, 4). Its visual
representation is below.
(-5, -1]  (2, 4)
-6
-4
-2
0
2
4
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
8.
6
Create a graph that has the following characteristics.
9. (2, ∞)
10. (-4, 0)  (2, 5].
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
11-14: For each number line, write the given set of numbers in interval notation and set notation.
11.
12.
Interval:
Interval:
Set:
Set:
13.
14.
Interval:
Interval:
Set:
Set:
15-17: For each inequality, (a) graph on a number line, (b) write in interval notation, and (c) write in
set notation.
15. x  4
16. x  1 or x  4
Graph:
Graph:
Interval:
Interval:
Set:
Set:
17. all real numbers from  23 to  4 , including  23 but not including  4 .
Graph:
Interval:
Set: