Math Problem Statement

Write the interval notation and set-builder notation for the given graph, where the graph represents all values greater than or equal to -10.

Solution

The graph represents all values greater than or equal to 10-10. Let's break it down:

  1. Interval Notation:
    Since the values start at 10-10 (inclusive) and extend to infinity (\infty), the interval notation is:
    [10,)[-10, \infty)

    • The square bracket [[] indicates that 10-10 is included.
    • The parenthesis (() for \infty shows that infinity is not a specific number and cannot be included.
  2. Set-Builder Notation:
    In set-builder notation, this can be written as:
    {xx10}\{x \mid x \geq -10\}
    (This reads: "The set of all xx such that xx is greater than or equal to 10-10.")


Let me know if you'd like additional explanations!

Here are 5 related questions for practice:

  1. What would the interval notation be for x<5x < 5?
  2. How do we represent x>0x > 0 using set-builder notation?
  3. What does the interval notation (,3](-\infty, 3] represent on a number line?
  4. How do we write xx such that xx is between 5-5 and 77 (inclusive) in interval notation?
  5. Can infinity (\infty) or negative infinity (-\infty) ever have a square bracket in interval notation? Why or why not?

Tip: When writing interval notation, always use parentheses with infinity (\infty) or negative infinity (-\infty) because they are not finite numbers!

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Math Problem Analysis

Mathematical Concepts

Inequalities
Interval Notation
Set-Builder Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8