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 $<$).