https://file.aiquickdraw.com/mathbot/file/1725938314634f291wwtr.jpg

The image shows the set notation:

\[
b = \{x \mid |x| \geq 5\}
\]

This represents the set of all real numbers \( x \) such that the absolute value of \( x \) is greater than or equal to 5.

### Interpretation:
- The absolute value \( |x| \geq 5 \) means that \( x \) is either less than or equal to \(-5\) or greater than or equal to \( 5 \).
  
In interval notation, this would be expressed as:
\[
x \in (-\infty, -5] \cup [5, \infty)
\]

This describes two disjoint intervals on the number line:
- \( x \leq -5 \) 
- \( x \geq 5 \)

Would you like any further details on this concept or have any questions?

### Related Questions:
1. How do we solve other inequalities involving absolute values?
2. What is the geometric interpretation of \( |x| \geq 5 \) on the number line?
3. Can you describe the difference between \( |x| > 5 \) and \( |x| \geq 5 \)?
4. How can we express the solution of \( |x| \leq 5 \) in set notation?
5. How do we handle compound inequalities involving absolute values, such as \( |x-2| \leq 4 \)?

**Tip:** Always remember that absolute value inequalities split into two cases: one for the positive and one for the negative side of the number line.

Learn how to solve the absolute value inequality |x| ≥ 5 and express it using interval notation. This problem covers key mathematical concepts in set notation, absolute value, and inequalities. Suitable for students in Grades 9-12.

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