Display the interval notation for:

7x≤21

Interval Notation Definition:

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

Build interval notation

We get interval notation by saying 7x≤21

Since our variable of x has a coefficient of 7
Divide each side of the inequality by 7

x≤3  ←Use this expression going forward

Inequality Sign Evaluation

You entered the ≤ sign

Build the interval notation for x:

Because you entered an equal sign
Translate to ] since we 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 -∞

Build notation

(-∞,3]

You have 1 free calculations remaining

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Set Builder Notation for x:

{ x | x≤3 } where | denotes such that

Display the literal notation for x

∞,...,-7,-6,-5,-4,-3,-2,-1,0,1,2,3

What is the Answer?

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

Interval Notation and Set Builder Notation Calculator Video

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