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 x6x \leq 6 in various forms, here's how it is done:

a) Number line representation:

On a number line, the inequality x6x \leq 6 means that all numbers less than or equal to 6 are included. On the number line:

  • A solid dot is placed at 66 to indicate that 66 is included.
  • An arrow extends to the left from 66 to represent all numbers less than 6.

b) Interval notation:

In interval notation, we express the range of values that satisfy the inequality: (,6](-\infty, 6] Here, -\infty represents that there is no lower bound (all negative numbers), and the square bracket ]] at 66 indicates that 66 is included.

c) Set builder notation:

In set builder notation, the inequality is written as: {xx6}\{ x \mid x \leq 6 \} This reads as "the set of all xx such that xx is less than or equal to 6."

Would you like a more detailed explanation of any part of this solution?

Related Questions:

  1. How would you express x>6x > 6 on a number line?
  2. What would the interval notation be for x>6x > 6?
  3. How would you represent x2x \geq -2 using set-builder notation?
  4. What is the difference between open and closed intervals?
  5. 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