Math Problem Statement

Write the interval notation and set-builder notation for the given graph. The graph shows a solid circle at -10, extending to the right with an arrow.

Solution

The graph represents a number line starting at 10-10, with a solid circle at 10-10, extending to the right (greater than or equal to 10-10).

Interval Notation:

The interval includes 10-10 and goes to positive infinity: [10,)[-10, \infty)

Set-Builder Notation:

The set of all numbers xx such that xx is greater than or equal to 10-10: {xx10}\{x \,|\, x \geq -10\}

Would you like a detailed explanation of how interval and set-builder notations work?

Here are 5 related questions to deepen your understanding:

  1. What does a solid circle on the graph signify compared to an open circle?
  2. How is infinity represented in interval notation, and why is it always open?
  3. What is the difference between [10,)[-10, \infty) and (10,)(-10, \infty)?
  4. Can you write an example of a set with both an upper and lower bound?
  5. How would the graph look if the inequality was x>10x > -10 instead of x10x \geq -10?

Tip: Always remember that infinity ()(\infty) and negative infinity ()(-\infty) are never included in interval notation because they are not actual 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 7-9