Question
Pablo is making a keychain that looks like Earth. He is using 13 green beads and plans to use more blue beads than green beads.
Let b represent the number of blue beads that Pablo might use. 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.
Let b represent the number of blue beads that Pablo might use. 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.
Answers
GPT-4o mini
To model the story, we know that Pablo has 13 green beads and wants to use more blue beads than green beads.
Let \( b \) represent the number of blue beads. Since he needs more blue beads than green beads, we can express this relationship as:
\[ b > 13 \]
This inequality states that the number of blue beads \( b \) must be greater than 13.
### Graphing the Inequality
To graph the inequality \( b > 13 \):
1. **Draw a number line**: Mark a horizontal line and label it with numbers surrounding 13.
2. **Mark the point 13**: Place a point at 13 on the number line. Since the inequality \( b > 13 \) does not include the value of 13, you should use an **open circle** at this point.
3. **Draw the ray**: From the open circle at 13, draw a ray extending to the right (toward greater numbers) to illustrate that \( b \) can be any number greater than 13.
The graph should look like this:
```
<---|---|---|---|---|---|---|---|---|---|---|--->
10 11 12 (13) 14 15 16 17 ...
```
In this graph:
- The circle at 13 is open to show that 13 is not included in the solution set.
- The arrow extends to the right, indicating that \( b \) can take any value greater than 13.
Let \( b \) represent the number of blue beads. Since he needs more blue beads than green beads, we can express this relationship as:
\[ b > 13 \]
This inequality states that the number of blue beads \( b \) must be greater than 13.
### Graphing the Inequality
To graph the inequality \( b > 13 \):
1. **Draw a number line**: Mark a horizontal line and label it with numbers surrounding 13.
2. **Mark the point 13**: Place a point at 13 on the number line. Since the inequality \( b > 13 \) does not include the value of 13, you should use an **open circle** at this point.
3. **Draw the ray**: From the open circle at 13, draw a ray extending to the right (toward greater numbers) to illustrate that \( b \) can be any number greater than 13.
The graph should look like this:
```
<---|---|---|---|---|---|---|---|---|---|---|--->
10 11 12 (13) 14 15 16 17 ...
```
In this graph:
- The circle at 13 is open to show that 13 is not included in the solution set.
- The arrow extends to the right, indicating that \( b \) can take any value greater than 13.