Let's carefully analyze the given expression to understand what the constant term represents.
1. Understanding the components of the expression:
The expression given is:
[tex]\[
90x - 20
\][/tex]
- Here, [tex]\(90x\)[/tex] represents the points Terrence scored from completing tasks, where [tex]\(x\)[/tex] is the number of tasks completed, and each task is worth 90 points.
- The term [tex]\(-20\)[/tex] is a constant term.
2. Identifying what each term represents:
- The term [tex]\(90x\)[/tex] represents the points scored for the tasks Terrence completed.
- The constant term [tex]\(-20\)[/tex] is a fixed value that modifies the total points.
3. Interpreting the constant term in context:
- In the context of the expression, the constant term [tex]\(-20\)[/tex] is subtracted from the total task points Terrence earned.
- This indicates that overall, Terrence’s total is 20 points less than what is directly calculated from the tasks.
4. Relating it to Shelly's points:
- Shelly's total points can be expressed as [tex]\(90x\)[/tex], where she scores 90 points for each of the [tex]\(x\)[/tex] tasks she completed.
- The term [tex]\(-20\)[/tex] in Terrence's expression [tex]\(90x - 20\)[/tex] demonstrates that Terrence scored 20 points fewer than Shelly.
Therefore, the constant term [tex]\(-20\)[/tex] represents the difference between Shelly's and Terrence's total points in the game.
In conclusion, the correct interpretation of the constant term [tex]\(-20\)[/tex] is:
"The difference between Shelly's and Terrence's total points," which is option:
```
The difference between Shelly's and Terrence's total points
```
