https://file.aiquickdraw.com/mathbot/file/1725376182219hdbwwbye.jpg

The equation provided in the image is:

\[
h = 3 - \frac{5}{k + 4}
\]

We need to solve for \( k \) in terms of \( h \).

### Steps to solve:

1. **Isolate the fraction** on one side of the equation:

   \[
   \frac{5}{k + 4} = 3 - h
   \]

2. **Invert both sides** to eliminate the fraction:

   \[
   k + 4 = \frac{5}{3 - h}
   \]

3. **Solve for \( k \)** by subtracting 4 from both sides:

   \[
   k = \frac{5}{3 - h} - 4
   \]

So, the value of \( k \) is:

\[
k = \frac{5}{3 - h} - 4
\]

Would you like further details or have any questions about this solution?

### Related Questions:

1. What happens to \( k \) when \( h = 0 \)?
2. How would the equation change if the fraction were added instead of subtracted from 3?
3. What are the limitations on \( h \) for \( k \) to be a real number?
4. Can you solve the equation if \( h = 1 \)?
5. How would you graph the relationship between \( k \) and \( h \)?

### Tip:
Always check the domain of your solution when working with fractions to avoid division by zero or undefined expressions.

Learn how to solve the equation h = 3 - 5/(k + 4) for k. This detailed step-by-step solution covers algebraic concepts, including isolating variables and manipulating fractions. Suitable for high school students in Grades 9-12.

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