Question
Javier is making 35 origami animals to hang in his bedroom. He's great at making swans, but he wants a variety of animals. Javier plans to make fewer than 15 swans.
Let s represent the number of swans Javier might make. 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 s represent the number of swans Javier might make. 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 represent Javier's origami animal-making situation with an inequality, we can define the variables based on the information given:
- \( s \): the number of swans Javier makes.
- The total number of origami animals he plans to create is 35.
- Javier plans to make fewer than 15 swans.
Putting this all together, we can set up the following inequality:
\[ s < 15 \]
However, since Javier is making a total of 35 animals, and the number of swans must be a non-negative integer (i.e., he cannot make a negative number of swans), we also include:
\[ s \geq 0 \]
The inequalities we are interested in can thus be represented as:
1. \( s < 15 \)
2. \( s \geq 0 \)
The effective modeling inequality for Javier's plan is:
\[ 0 \leq s < 15 \]
### Graphing the Inequality
To graph the inequality \( 0 \leq s < 15 \):
1. **Draw a number line.**
- Mark points 0 and 15 on the number line.
2. **Represent the interval:**
- Since \( s \) can take any value from 0 to just below 15:
- Use a closed dot at \( 0 \) to indicate that 0 is included in the range (i.e., \( s \geq 0\)).
- Use an open dot at \( 15 \) to indicate that 15 is not included in the range (i.e., \( s < 15\)).
- Shade the line between these two points to represent the range of \( s \).
Putting these elements together visualizes that the number of swans Javier can make (s) is between 0 and just below 15.
- \( s \): the number of swans Javier makes.
- The total number of origami animals he plans to create is 35.
- Javier plans to make fewer than 15 swans.
Putting this all together, we can set up the following inequality:
\[ s < 15 \]
However, since Javier is making a total of 35 animals, and the number of swans must be a non-negative integer (i.e., he cannot make a negative number of swans), we also include:
\[ s \geq 0 \]
The inequalities we are interested in can thus be represented as:
1. \( s < 15 \)
2. \( s \geq 0 \)
The effective modeling inequality for Javier's plan is:
\[ 0 \leq s < 15 \]
### Graphing the Inequality
To graph the inequality \( 0 \leq s < 15 \):
1. **Draw a number line.**
- Mark points 0 and 15 on the number line.
2. **Represent the interval:**
- Since \( s \) can take any value from 0 to just below 15:
- Use a closed dot at \( 0 \) to indicate that 0 is included in the range (i.e., \( s \geq 0\)).
- Use an open dot at \( 15 \) to indicate that 15 is not included in the range (i.e., \( s < 15\)).
- Shade the line between these two points to represent the range of \( s \).
Putting these elements together visualizes that the number of swans Javier can make (s) is between 0 and just below 15.