https://file.aiquickdraw.com/mathbot/file/1728279834533fdrptbiv.jpg

The problem asks to:

1. Graph the set \( \{x \mid 0 \leq x \leq 6 \} \) on a number line.
2. Write the set using interval notation.

### Step 1: Graph the Set on a Number Line
The inequality \( 0 \leq x \leq 6 \) means that \( x \) includes all numbers between 0 and 6, including the endpoints 0 and 6. On the number line, we can represent this by:
- A solid dot at 0, indicating that 0 is included.
- A solid dot at 6, indicating that 6 is included.
- A line connecting 0 and 6, showing that all values between 0 and 6 are included.

### Step 2: Write the Set in Interval Notation
In interval notation, the set \( \{x \mid 0 \leq x \leq 6 \} \) is written as:
\[
[0, 6]
\]
The square brackets \( [ \) and \( ] \) indicate that both endpoints (0 and 6) are included in the set.

Would you like me to sketch the graph, or do you need further details on how this interval works? Feel free to ask for more!

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### Relative Questions:
1. How would the interval notation change if \( x = 6 \) were excluded?
2. Can you express the same set in set-builder notation instead of interval notation?
3. How would this set change if we were working in \( x > 0 \) and \( x \leq 6 \)?
4. What is the difference between square brackets and parentheses in interval notation?
5. How do you interpret inequalities with infinity when writing in interval notation?

**Tip:** When writing intervals, square brackets \( [ ] \) include the endpoint, while parentheses \( ( ) \) exclude it.

Graph the set {x | 0 ≤ x ≤ 6} on the number line. Then, write the set using interval notation.

Learn how to graph the set {x | 0 ≤ x ≤ 6} on a number line and express it using interval notation. This guide covers the key mathematical concepts of inequalities and graphing, perfect for students in Grades 6-8.

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