Display the interval notation for:

150p≤3000

An interval as a set of numbers.

Numbers = endpoints.

We get interval notation by saying 150p≤3000

Since our variable of p has a coefficient of 150

Divide each side of the inequality by 150

150p | |

150 |

≤ |

3000 |

150 |

p≤20 ←Use this expression going forward

You entered the ≤ sign

Because you entered an equal sign

Translate to ] since we include the number 20

Based on the ≤ you entered,

the left side of the interval notation will extend to negative infinity,

which is denoted as -∞

**{ p | p≤20 }** where | denotes *such that*

**∞,...,10,11,12,13,14,15,16,17,18,19,20**

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.

* 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.

Equal sign means you use a brace

No equal sign means you use a parentheses

For more math formulas, check out our Formula Dossier

No equal sign means you use a parentheses

For more math formulas, check out our Formula Dossier

- 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

- 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]

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