To solve the function \( f(x) = 3x - 7 \) for \( x = 35 \) and \( x = 100 \), we need to substitute the values of \( x \) into the function and calculate the results.

1. **For \( x = 35 \):**
   \[
   f(35) = 3(35) - 7
   \]
   \[
   f(35) = 105 - 7
   \]
   \[
   f(35) = 98
   \]

2. **For \( x = 100 \):**
   \[
   f(100) = 3(100) - 7
   \]
   \[
   f(100) = 300 - 7
   \]
   \[
   f(100) = 293
   \]

So, the solutions are:
- \( f(35) = 98 \)
- \( f(100) = 293 \)

Would you like any further details or have any questions?

Here are some related questions to expand your understanding:

1. How would you solve \( f(x) = 3x - 7 \) for a general value of \( x \)?
2. What is the value of \( f(x) \) when \( x = 0 \)?
3. How would the function change if the constant term was different, say \( f(x) = 3x + 5 \)?
4. What is the inverse function of \( f(x) = 3x - 7 \)?
5. How does the slope of the function \( f(x) = 3x - 7 \) compare to other linear functions?
6. What are the intercepts of the function \( f(x) = 3x - 7 \)?
7. How do you graph the function \( f(x) = 3x - 7 \)?
8. What is the domain and range of the function \( f(x) = 3x - 7 \)?

**Tip:** Always double-check your calculations to ensure accuracy, especially when substituting values into functions.

Learn how to solve the linear function f(x) = 3x - 7 for specific values of x (35 and 100) with detailed step-by-step calculations. This problem involves linear functions, substitution method, and arithmetic operations. Suitable for students in Grades 6-8.

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