https://file.aiquickdraw.com/mathbot/file/172384016222394fxjgbu.jpg

Let's solve the problem step by step based on the procedure given in the image.

### Problem Breakdown
The function transforms an input value \( x \) into an output value following these steps:
1. **Step 1:** Multiply the input value by 6.
2. **Step 2:** Add 8 to the result.
3. **Step 3:** Divide this result by 4.

The output from this function is 15 when the input is 7. We need to determine the value of \( x \) that satisfies this condition.

### Let's solve it:

1. **Multiply the input by 6:**
   \[
   6x
   \]
   
2. **Add 8 to this result:**
   \[
   6x + 8
   \]
   
3. **Divide this result by 4:**
   \[
   \frac{6x + 8}{4}
   \]
   
Given that this expression equals 15 when \( x = 7 \):

\[
\frac{6(7) + 8}{4} = 15
\]

### Simplifying:
- Multiply \( 7 \) by 6:
  \[
  6 \times 7 = 42
  \]
- Add 8:
  \[
  42 + 8 = 50
  \]
- Divide by 4:
  \[
  \frac{50}{4} = 12.5
  \]

This does not yield the expected output of 15. Let's instead solve for \( x \) directly using the equation:

\[
\frac{6x + 8}{4} = 15
\]

### Solving for \( x \):

1. Multiply both sides by 4:
   \[
   6x + 8 = 60
   \]
2. Subtract 8 from both sides:
   \[
   6x = 52
   \]
3. Divide by 6:
   \[
   x = \frac{52}{6} \approx 8.67
   \]

So, \( x \) is approximately \( 8.67 \).

However, if \( x = 7 \) was meant to be the correct value for the output of 15, then there might be an error in the problem's conditions. Would you like to revisit the calculations or explore more options?

---

**Questions for Further Exploration:**

1. How can you set up an equation based on a function's steps?
2. How do you handle discrepancies in expected vs. calculated results?
3. What techniques help verify the correctness of a calculated result?
4. Can this function be inverted to solve for \( x \) directly?
5. How can functions be tested with multiple inputs to ensure accuracy?
6. What is the importance of double-checking each step in a multi-step function?
7. How do rounding errors impact the final output in such problems?
8. Can different methods be used to approximate the value of \( x \) more accurately?

**Tip:** Always double-check each step when working through multi-step problems, as small errors can compound and lead to incorrect results.

Explore how to solve a function transformation problem step-by-step. This problem involves arithmetic operations and equation solving techniques. Suitable for students in Grades 9-12.

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