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 -∞
Final Answer
(-∞,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
Common Core State Standards In This Lesson
CCSS.MATH.CONTENT.6.EE.B.8
What is the Answer?
(-∞,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.
* 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
