Math Problem Statement

Which set describes the graph?

Solution

The graph shows a highlighted section between x=2x = 2 and x=3x = 3, inclusive on both endpoints. This is represented by the solid dots at both 2 and 3, indicating that these points are included in the solution set.

From this, the correct set notation should include both x=2x = 2 and x=3x = 3 as boundaries with \leq and \geq.

Thus, the correct choice is:
{x2x3}\{ x \mid 2 \leq x \leq 3 \}

This set means that xx is greater than or equal to 2, and less than or equal to 3.

Would you like further details or explanations?

Here are 5 questions related to this topic:

  1. What does it mean when a dot is solid on a number line?
  2. How do we represent an open interval on a graph?
  3. Can you explain the difference between "and" and "or" in set notation?
  4. How do we convert set notation to interval notation?
  5. What kind of inequality would describe a union of two intervals?

Tip: Solid dots on a number line mean that the endpoints are included in the interval (using \leq or \geq).

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Math Problem Analysis

Mathematical Concepts

Set Notation
Inequalities
Number Line

Formulas

x ≥ 2 and x ≤ 3

Theorems

Set Theory

Suitable Grade Level

Grades 6-8