Given f, of, x, equals, 5, x, plus, 4f(x)=5x+4, solve for xx when f, of, x, equals, minus, 6f(x)=−6.

You are given the function \( f(x) = 5x + 4 \), and you're asked to find \( x \) when \( f(x) = -6 \).

### Steps to solve:

1. Start with the equation for \( f(x) \):
   \[
   f(x) = 5x + 4
   \]
   
2. Set \( f(x) = -6 \) since that’s the given condition:
   \[
   5x + 4 = -6
   \]

3. Solve for \( x \):

   - Subtract 4 from both sides:
     \[
     5x = -6 - 4
     \]
     \[
     5x = -10
     \]

   - Divide both sides by 5:
     \[
     x = \frac{-10}{5}
     \]
     \[
     x = -2
     \]

So, \( x = -2 \).

Would you like a more detailed explanation or have any questions?

### Related Questions:
1. What if \( f(x) = 0 \)? What is the value of \( x \)?
2. How would the solution change if \( f(x) = 10 \)?
3. Can you find the inverse function of \( f(x) = 5x + 4 \)?
4. What is the slope of the linear function \( f(x) = 5x + 4 \)?
5. What would \( x \) be if the equation was \( f(x) = 5x - 4 \)?

### Tip:
When solving for \( x \), always perform inverse operations to isolate \( x \) step-by-step.

Given f(x) = 5x + 4, solve for x when f(x) = -6.

Find the value of x in the linear function f(x) = 5x + 4 when f(x) = -6 with a detailed solution. This problem involves key algebra concepts, including solving linear equations. Suitable for students in Grades 6-8.

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