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
| 7x | |
| 7 |
| ≤ |
| 21 |
| 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 -∞
Final Answer
(-∞,3]
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
Common Core State Standards In This Lesson
CCSS.MATH.CONTENT.6.EE.B.8
What is the Answer?
(-∞,3]
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.
* 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
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
