Math Problem Statement
Express the following inequality a) using a number line, b) in interval notation, and c) as a solution set (use set builder notation). x less than or equals 6
Solution
To express the inequality in various forms, here's how it is done:
a) Number line representation:
On a number line, the inequality means that all numbers less than or equal to 6 are included. On the number line:
- A solid dot is placed at to indicate that is included.
- An arrow extends to the left from to represent all numbers less than 6.
b) Interval notation:
In interval notation, we express the range of values that satisfy the inequality: Here, represents that there is no lower bound (all negative numbers), and the square bracket at indicates that is included.
c) Set builder notation:
In set builder notation, the inequality is written as: This reads as "the set of all such that is less than or equal to 6."
Would you like a more detailed explanation of any part of this solution?
Related Questions:
- How would you express on a number line?
- What would the interval notation be for ?
- How would you represent using set-builder notation?
- What is the difference between open and closed intervals?
- How do you represent compound inequalities using interval notation?
Tip: In interval notation, use a square bracket [ ] when the endpoint is included (closed), and a parenthesis ( ) when it’s not included (open).
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Math Problem Analysis
Mathematical Concepts
Inequalities
Number Line
Interval Notation
Set Builder Notation
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8