Question
Every year, Oakwood Community Center holds a bike-a-thon to raise money for charity. Last year, Charlie biked a total of 28.5 miles. He's set a goal to bike at least as many miles this year as he did last year.
Let m represent the distance, in miles, that Charlie wants to bike this year. Which inequality models the story?
Graph the inequality that
Let m represent the distance, in miles, that Charlie wants to bike this year. Which inequality models the story?
Graph the inequality that
Answers
GPT-4o mini
To represent the story using an inequality, we need to express the relationship between the distance Charlie wants to bike this year (m) and the distance he biked last year (28.5 miles). Since he wants to bike at least as many miles this year as he did last year, we can write the inequality as:
\[ m \geq 28.5 \]
This inequality states that the distance \( m \) must be greater than or equal to 28.5 miles.
### Graphing the Inequality
To graph the inequality \( m \geq 28.5 \):
1. **Draw a number line**:
- Label the number line with relevant mileage values. Ensure 28.5 is marked clearly.
2. **Plot the point**:
- Place a solid dot on 28.5. The solid dot signifies that 28.5 is included in the solution (since it is "at least as many").
3. **Shade the region**:
- Shade to the right of 28.5. This shading represents all the values of \( m \) that are greater than 28.5.
The final graph visually shows the allowed values for \( m \), starting from 28.5 and continuing to infinity. The solution set includes all the distances Charlie could aim for this year, which are 28.5 miles and above.
\[ m \geq 28.5 \]
This inequality states that the distance \( m \) must be greater than or equal to 28.5 miles.
### Graphing the Inequality
To graph the inequality \( m \geq 28.5 \):
1. **Draw a number line**:
- Label the number line with relevant mileage values. Ensure 28.5 is marked clearly.
2. **Plot the point**:
- Place a solid dot on 28.5. The solid dot signifies that 28.5 is included in the solution (since it is "at least as many").
3. **Shade the region**:
- Shade to the right of 28.5. This shading represents all the values of \( m \) that are greater than 28.5.
The final graph visually shows the allowed values for \( m \), starting from 28.5 and continuing to infinity. The solution set includes all the distances Charlie could aim for this year, which are 28.5 miles and above.