Question

On weekends, Roxanne likes to participate in skateboard competitions. She has learned a total of 28 different tricks. On some days, Roxanne will do all of her tricks during a competition. On other days, she only has time to do some of them.
Let t represent the number of tricks Roxanne might do during a competition. Which inequality models the story?
Graph the inequality that models the story.

Answer 1

To model the story with an inequality, we want to express the relationship between the number of tricks \( t \) that Roxanne can do during a competition and the total number of tricks she knows, which is 28. The number of tricks she can do must be a non-negative quantity and cannot exceed the total number of tricks she knows.

Thus, we can express this as:
\[
0 \leq t \leq 28
\]

This can be split into two inequalities:
1. \( t \geq 0 \) (Roxanne cannot perform a negative number of tricks)
2. \( t \leq 28 \) (Roxanne cannot perform more tricks than she knows)

Combining these, we have the inequality:
\[
0 \leq t \leq 28
\]

### Graphing the Inequality

To graph this inequality on a number line:

1. Draw a number line.
2. Mark the points 0 and 28 on the number line.
3. Use a solid dot or a closed circle at 0 and 28 to indicate that both endpoints are included in the solution set.
4. Shade the region between the two points to represent all values of \( t \) that satisfy \( 0 \leq t \leq 28 \).

Here's a textual representation of what the graph will approximately look like:

```
<---|----|----|----|----|----|----|----|----|----|----|----|----|----|----|--->
-2 -1 0 1 2 3 ... 25 26 27 28 29 30
●----------------------------●
```

In this representation:
- The dots at 0 and 28 imply that those values are included in the solution.
- The shaded area between the two points indicates all possible values of \( t \) that Roxanne can perform, from 0 tricks to a maximum of 28 tricks.