To determine the distance she travels in a week, let's analyze the given options step-by-step.
1. Option 1: [tex]\( \frac{x}{7} \)[/tex]
- This option suggests dividing the daily distance ([tex]\(x\)[/tex]) by 7. This calculation would result in the average distance traveled per day over the course of a week. Hence, it calculates how much distance she travels in one day if the total for the week is spread evenly, which is not what we're looking for.
2. Option 2: [tex]\( x + 7 \)[/tex]
- This option implies adding 7 units to the daily distance ([tex]\(x\)[/tex]). However, this doesn't fit logically since it suggests adding a constant number to the daily travel rather than multiplying by the number of days in a week.
3. Option 3: [tex]\( 7x \)[/tex]
- This option suggests multiplying the daily distance ([tex]\(x\)[/tex]) by 7, which makes the most sense because it accumulates the distance traveled over each day of the week. If she travels [tex]\( x \)[/tex] units every day, then over 7 days, she would travel [tex]\( 7x \)[/tex] units.
4. Option 4: [tex]\( 7 - x \)[/tex]
- This option suggests subtracting the daily distance ([tex]\(x\)[/tex]) from 7, which doesn't logically represent the total weekly distance traveled. It doesn't fit the context of calculating cumulative distance.
By evaluating these options, we see that only [tex]\( 7x \)[/tex] correctly represents the total distance traveled in a week, considering she travels [tex]\( x \)[/tex] units per day for 7 days.
Therefore, the distance she travels in a week is:
[tex]\[ 7x \][/tex]
Given the numerical result from the earlier method being 3, the valid option corresponds to [tex]\( 7x \)[/tex]. Thus the correct answer is the third option:
[tex]\[ 7x \][/tex]
