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The problem is asking us to solve for \( x \) given the function \( f(x) = -3x + 3 \) when \( f(x) = 9 \).

Here’s how we can solve it step-by-step:

1. Start with the given equation:
   \[
   f(x) = -3x + 3
   \]

2. Substitute \( f(x) = 9 \) into the equation:
   \[
   9 = -3x + 3
   \]

3. Subtract 3 from both sides to isolate the term with \( x \):
   \[
   9 - 3 = -3x
   \]
   \[
   6 = -3x
   \]

4. Divide both sides by \(-3\) to solve for \( x \):
   \[
   x = \frac{6}{-3}
   \]
   \[
   x = -2
   \]

So, the solution is:
\[
\boxed{x = -2}
\]

Would you like further explanation or have any questions?

Here are some related questions you might be interested in:
1. How do you solve linear equations involving functions?
2. What is the impact of negative coefficients on function graphs?
3. How do you graph the function \( f(x) = -3x + 3 \)?
4. What are the steps to solve an equation when given a function value?
5. How can changes to constants affect the position of a function graph?

**Tip:** Always check your solution by substituting the value of \( x \) back into the original function to verify it satisfies the given condition.

Given f(x) = -3x + 3, solve for x when f(x) = 9.

Discover how to solve the linear equation f(x) = -3x + 3 for x when f(x) = 9. This problem involves key algebraic concepts like linear functions and properties of linear equations. Suitable for students in Grades 7-9.

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