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Enter inequality for interval notation:


  
Display the interval notation for:
x≤5

Interval Notation Definition:

An interval as a set of numbers.
Numbers = endpoints.
You entered the ≤ sign
Start on the right side of x<=5

Build the interval notation for x:

An equal sign translates to ]
Include the number 5.
The left side extends to -∞




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Set Builder Notation for x:

{ x | x≤5 } where | denotes such that


Display the literal notation for x

∞,...,-5,-4,-3,-2,-1,0,1,2,3,4,5


What is the Answer?

(-∞,5]

How does the Interval Notation and Set Builder Notation Calculator work?

Free Interval Notation and Set Builder Notation Calculator - This calculator translates the following inequality statements to interval notation and set builder notation:
* 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?

Equal sign means you use a brace
No equal sign means you use a parentheses

For more math formulas, check out our Formula Dossier

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

  1. x<5
  2. x<=5
  3. q>5
  4. z>=5
  5. a<0 or a>5
  6. 2 <= x <= 20
  7. -4x<0
  8. 9j>36
  9. |x|<3
  10. x<7 and x>-4
  11. {x | -1 >x >-10}
  12. 2 through 7 inclusive
  13. x<5 or >-5
  14. {x|x<1}
  15. 2 is less than or equal to x is less than or equal to 8
  16. natural numbers greater than 4
  17. whole numbers less than 10
  18. integers less than or equal to 27
  19. x<>5
  20. {x|x<>0}
  21. w not equal to 8
  22. [2,infinity]

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