Display the interval notation for:
|x|<3
Interval Notation Definition:
An interval as a set of numbers.
Numbers = endpoints.
Absolute Value Procedure
Because we have an absolute value
We have two equations that we form:
- x<(c)
- x>-(c)
Given this, we form our two equations:
- x<3
- x>-3
In interval notation, express as an or statement
Account for or
Since we have an or statement
We break this up into two pieces
Piece 1 → x<3
Piece 2 → x>-3
Evaluate Piece 1
Inequality Sign Evaluation
You entered the < sign
Build the interval notation for x:
No equal sign translates to ).
Do not include the number 3
Based on the < you entered,
the left side of the interval notation will extend to negative infinity,
which is denoted as -∞
Final Answer
Set Builder Notation for x:
{ x | x<3 } where | denotes such that
Evaluate Piece 2
Inequality Sign Evaluation
You entered the < sign
Build the interval notation for x:
No equal sign translates to (.
Do not include the number -3
Based on the < you entered,
the right side of the interval notation will extend to positive infinity,
which is denoted as +∞
Final Answer
Set Builder Notation for x:
{ x | x<3 } where | denotes such that
Form our interval notation for x:
(-∞,3) U (-3,+∞)
Display the literal notation for x
-2,-1,0,1,2,3,4,5,6,7,...,∞
Common Core State Standards In This Lesson
What is the Answer?
How does the Interval Notation and Set Builder Notation Calculator work?
* x < 5
* y <= 5
* z > 5
* a >= 5
* b < 5 or b > 20
* Compound Inequality such as 0 <= c < 4
* |x|<3
* Reverse Interval Notation to Inequality Statement such as (-7,5]
* {x|x<1}
* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8
This calculator has 2 inputs.
What 2 formulas are used for the Interval Notation and Set Builder Notation Calculator?
No equal sign means you use a parentheses
What 10 concepts are covered in the Interval Notation and Set Builder Notation Calculator?
- domain
- Set of all possible input values which makes the output value of a function valid
- equal
- being the same in quantity, size, degree, or value
= - greater than
- Shows an inequality of one value being more than another
> - inequality
- a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
>, <, ≤, ≥ - interval
- a set of real numbers that contains all real numbers lying between any two numbers of the set
- interval notation
- a method to represent an interval on a number line using subsets of the real numbers
- interval notation and set builder notation
- less than
- Shows an inequality of one value being less than another
< - notation
- An expression made up of symbols for representing operations, unspecified numbers, relations and any other mathematical objects
- range
- Difference between the largest and smallest values in a number set
Example calculations for the Interval Notation and Set Builder Notation Calculator
- x<5
- x<=5
- q>5
- z>=5
- a<0 or a>5
- 2 <= x <= 20
- -4x<0
- 9j>36
- |x|<3
- x<7 and x>-4
- {x | -1 >x >-10}
- 2 through 7 inclusive
- x<5 or >-5
- {x|x<1}
- 2 is less than or equal to x is less than or equal to 8
- natural numbers greater than 4
- whole numbers less than 10
- integers less than or equal to 27
- x<>5
- {x|x<>0}
- w not equal to 8
- [2,infinity]
