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.