Given f, of, x, equals, minus, x, plus, 3f(x)=−x+3, solve for xx when f, of, x, equals, 4f(x)=4.

We are given the equation \( f(x) = -x + 3 \) and asked to solve for \( x \) when \( f(x) = 4 \).

### Step-by-step solution:

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

2. Substitute \( f(x) = 4 \) into the equation:
   \[
   4 = -x + 3
   \]

3. Solve for \( x \):
   - Subtract 3 from both sides:
     \[
     4 - 3 = -x
     \]
     \[
     1 = -x
     \]

   - Multiply both sides by -1:
     \[
     x = -1
     \]

Thus, \( x = -1 \).

### Final answer:
\( x = -1 \).

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. What happens if we change \( f(x) \) to a quadratic function?
2. How would you solve \( f(x) = -x + 5 \) when \( f(x) = 6 \)?
3. What is the domain and range of the function \( f(x) = -x + 3 \)?
4. How do we interpret the slope and intercept of the linear function \( f(x) = -x + 3 \)?
5. Can you express \( x \) in terms of \( f(x) \) from \( f(x) = -x + 3 \)?

**Tip:** When solving linear equations, isolating the variable is key. Simplify the equation step by step!

Given f(x) = -x + 3, solve for x when f(x) = 4.

Learn how to solve the linear equation f(x) = -x + 3 when f(x) = 4 with a detailed step-by-step guide. This problem involves key algebraic concepts, including linear equations and solving for variables. Ideal for students in Grades 6-8.

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