Math Problem Statement

Graph the set \( \{x \mid x \geq 5\} \) on the number line. Then, write the set using interval notation.

Solution

For the given problem {xx5}\{x \mid x \geq 5\}, you need to represent it on the number line and write it in interval notation.

  1. Graph on the Number Line:

    • Since x5x \geq 5, draw a closed dot (●) at 5 to indicate that 5 is included in the solution.
    • Shade the number line to the right of 5 to show all numbers greater than or equal to 5.
  2. Interval Notation:

    • The interval notation for x5x \geq 5 is [5,)[5, \infty), where the square bracket [ indicates that 5 is included, and the parenthesis ) indicates that infinity is not included.

You should:

  • Place a closed dot at 5 on the number line and shade to the right.
  • Input the interval notation [5,)[5, \infty) in the provided box.

Would you like more details or have any questions about this process? Here are some related questions for further exploration:

  1. How do you graph x>5x > 5 on the number line, and what is its interval notation?
  2. What would be the interval notation for x2x \leq -2?
  3. How can we represent x<3x < 3 in set-builder notation?
  4. What is the interval notation for an inequality 3<x4-3 < x \leq 4?
  5. How do you handle compound inequalities like 1<x61 < x \leq 6 in interval notation?

Tip: Remember, closed dots indicate that the number is included in the set, while open dots indicate that it is not.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Set Notation
Interval Notation

Formulas

None

Theorems

None

Suitable Grade Level

Grades 7-10