Express the interval using two different representations x greater than or equal to 3 in interval notation and number line

To express the interval \( x \geq 3 \) in both interval notation and on a number line, follow these steps:

### 1. Interval Notation
- **Given Condition:** \( x \geq 3 \)
- **Interval Notation:** The interval notation for this condition is \([3, \infty)\).
  - The square bracket \([ \) indicates that 3 is included in the interval.
  - The infinity symbol \( \infty \) always uses a parenthesis \( ) \) because infinity is not a specific number and can't be included.

### 2. Number Line Representation
On the number line:
- Draw a line.
- Place a closed circle or dot at 3 to indicate that 3 is included in the interval.
- Shade the line to the right of 3, extending indefinitely, to represent all numbers greater than or equal to 3.

Here's how you can visualize it:

- **Number Line:**
  ```
  |----|----|----|----|----|----|----|----|----|---->
  0    1    2    3    4    5    6    7    8    9   ...
                                ●------------------>
                               3
  ```

This number line shows that all values from 3 to infinity are included in the interval.

Would you like more details or have any other questions? Here are some related questions that might help:

1. How would you represent \( x > 3 \) in interval notation and on the number line?
2. What does \( (-\infty, 3] \) represent, and how would it look on a number line?
3. How do you represent \( x \leq -2 \) using interval notation?
4. What is the difference between \( [3, \infty) \) and \( (3, \infty) \) in terms of number line representation?
5. Can you represent the interval \( [0, 5) \) on a number line?

**Tip:** When drawing intervals on a number line, remember to use a closed circle (●) for included endpoints (like \( \geq \) or \( \leq \)) and an open circle (○) for excluded endpoints (like \( > \) or \( < \)).

Learn how to express the interval x ≥ 3 using interval notation and on a number line with detailed steps and visual representations. This problem covers concepts in inequalities and number line representation, suitable for students in Grades 6-8.

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