##### Enter inequality for interval notation:

Display the interval notation for:

12s≤51

##### Interval Notation Definition:

An interval as a set of numbers.
Numbers = endpoints.

##### Build interval notation

We get interval notation by saying 12s≤51

Since our variable of s has a coefficient of 12
Divide each side of the inequality by 12

 12s 12
 ≤
 51 12

s≤4.25  ←Use this expression going forward

##### Inequality Sign Evaluation

You entered the ≤ sign

##### Build the interval notation for s:

Because you entered an equal sign
Translate to ] since we include the number 4.25

Based on the ≤ you entered,
the left side of the interval notation will extend to negative infinity,
which is denoted as -∞

(-∞,4.25]

##### Set Builder Notation for s:

{ s | s≤4.25 } where | denotes such that

##### Display the literal notation for s

∞,...,-5.75,-4.75,-3.75,-2.75,-1.75,-0.75,0.25,1.25,2.25,3.25,4.25

(-∞,4.25]
##### 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