Question

Gabrielle is going to be a robot for Halloween this year. She will make her costume out of cardboard boxes and rubber tubing from the hardware store. Gabrielle wants to make sure she has enough tubing, so she plans to buy at least 36 inches of it.
Let t represent the length of tubing, in inches, that Gabrielle might buy. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To model the story using the variable \( t \), we want to represent Gabrielle's requirement for tubing. She wants to buy at least 36 inches of tubing, which can be written as:

\[
t \geq 36
\]

This inequality indicates that the length of tubing \( t \) must be greater than or equal to 36 inches.

### Graphing the Inequality

To graph the inequality \( t \geq 36 \):

1. **Draw a horizontal number line**: This will represent the length of tubing in inches.
2. **Locate the number 36 on this line**.
3. **Since the inequality is \( t \geq 36 \)**, draw a **closed circle** at the 36 mark to indicate that it is included in the solution (since Gabrielle can buy exactly 36 inches or more).
4. **Shade the line to the right of 36**: This indicates that any value greater than 36 is also part of the solution set.

Here are the steps to represent it visually:

1. **Number Line**: Draw a horizontal line and label it with numbers. Ensure 36 is marked clearly.
2. **Closed Circle**: Place a closed circle on 36 to show it's included in the solution.
3. **Arrow/Shade to the right**: Draw a ray (arrow) that continues to the right of 36, indicating all values greater than 36 are part of the solution.

If using a graphing tool:
- Select the point at 36 and make it closed.
- Extend the line to the right with an arrow pointing further out.

This concludes the inequality representation and its graph.