Question

Brad has a solo performance in his orchestra's spring concert. Yesterday, he practiced his violin for 20 minutes. Today, Brad plans to practice even longer than yesterday.
Let t represent the length of time, in minutes, that Brad might practice today. 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 represent the story in the form of an inequality, we know that Brad practiced for 20 minutes yesterday and he plans to practice even longer today. This means we can express the inequality as:

\[ t > 20 \]

where \( t \) represents the length of time (in minutes) that Brad might practice today.

### Steps to Graph the Inequality:

1. **Number Line:** Begin by drawing a horizontal line to represent the number line.
2. **Mark the Point:** Locate and mark the point for 20 on the number line.
3. **Open Circle:** Since the inequality is "greater than" (and not "greater than or equal to"), use an open circle at the point 20 to indicate that 20 is not included in the solutions.
4. **Ray:** Draw a ray that extends to the right from the open circle to indicate all values greater than 20.

The graph will look something like this:

- An open circle at the point 20.
- A shaded line (or arrow) extending to the right from 20, indicating all values greater than 20.

This visualization correctly represents the inequality \( t > 20 \).