Sure! Let's take a closer look at the given problem and the expression representing Terrence's total points:
The expression provided is [tex]\( 90x - 20 \)[/tex].
We need to determine what the first term of this expression, [tex]\( 90x \)[/tex], represents. Here is a detailed, step-by-step explanation:
1. Understanding the expression [tex]\( 90x - 20 \)[/tex]:
- [tex]\( 90x \)[/tex]: This term is related to the total number of points earned by Shelly.
- [tex]\( -20 \)[/tex]: This suggests that Terrence earned 20 points less than Shelly.
2. Analyzing the context:
- Shelly and Terrence completed [tex]\( x \)[/tex] tasks in a game.
- The expression [tex]\( 90x - 20 \)[/tex] is used to calculate Terrence's total points, which is 20 points less than Shelly’s total points.
3. Interpreting the relation between Shelly's and Terrence's points:
- The [tex]\( 90x \)[/tex] in [tex]\( 90x - 20 \)[/tex] must be the total points Shelly earned, because when you subtract 20 from [tex]\( 90x \)[/tex], you get Terrence's points.
- Therefore, [tex]\( 90x \)[/tex] represents the total points Shelly earned.
4. Identifying the significance of [tex]\( 90x \)[/tex]:
- [tex]\( 90 \)[/tex] is the coefficient of [tex]\( x \)[/tex], indicating that Shelly earns 90 points per task.
- Since Shelly completed [tex]\( x \)[/tex] tasks, her total points are calculated as [tex]\( 90 \cdot x = 90x \)[/tex].
By considering these steps, we conclude that the first term of the expression [tex]\( 90x - 20 \)[/tex], which is [tex]\( 90x \)[/tex], represents the total points Shelly earned.
Thus, the correct choice is:
- The total points Shelly earned.
