To determine what the first term of the expression [tex]\(90x - 20\)[/tex] represents, let's analyze the given information step-by-step:
1. We know that Shelly and Terrence completed [tex]\(x\)[/tex] tasks in a game.
2. Terrence's total points are represented by the expression [tex]\(90x - 20\)[/tex].
3. Additionally, it is mentioned that Terrence's total points were 20 less than Shelly's total points.
Given that Terrence's points are 20 less than Shelly's, we can express Shelly's points mathematically as follows:
[tex]\[ \text{Shelly's points} = \text{Terrence's points} + 20 \][/tex]
Substitute Terrence's points ([tex]\(90x - 20\)[/tex]) into the equation:
[tex]\[ \text{Shelly's points} = (90x - 20) + 20 \][/tex]
Simplify the equation:
[tex]\[ \text{Shelly's points} = 90x - 20 + 20 \][/tex]
[tex]\[ \text{Shelly's points} = 90x \][/tex]
Thus, we find that Shelly's total points are expressed by the term [tex]\(90x\)[/tex].
Therefore, the first term of the expression ([tex]\(90x\)[/tex]) represents the total points Shelly earned.
So, the correct answer is:
a) The total points Shelly earned
