To find the total distance that the car was tested, we need to sum the distances driven on flat, downhill, and uphill roads. Let's break this down step by step.
1. Identify the given distances:
- Flat road distance: [tex]\( x \)[/tex] miles
- Downhill distance: [tex]\( x^2 + 3 \)[/tex] miles
- Uphill distance: [tex]\( x - 7 \)[/tex] miles
2. Sum the distances:
[tex]\[
\text{Total Distance} = (\text{Flat Road Distance}) + (\text{Downhill Distance}) + (\text{Uphill Distance})
\][/tex]
Substitute the given expressions:
[tex]\[
\text{Total Distance} = x + (x^2 + 3) + (x - 7)
\][/tex]
3. Combine like terms:
[tex]\[
\text{Total Distance} = x + x^2 + 3 + x - 7
\][/tex]
Combine the [tex]\(x\)[/tex] terms and the constants:
[tex]\[
\text{Total Distance} = x^2 + x + x + 3 - 7
\][/tex]
[tex]\[
\text{Total Distance} = x^2 + 2x - 4
\][/tex]
4. Simplified expression:
The simplified expression for the total distance is:
[tex]\[
x^2 + 2x - 4
\][/tex]
So, the correct answer is:
[tex]\[
x^2 + 2x - 4
\][/tex]
From the given options, the answer is:
[tex]\[
\boxed{x^2 + 2x - 4}
\][/tex]
