Let's solve the equation:

\[
9(k - 4) - 7k = 32 - 2(k + 8)
\]

### Step 1: Expand both sides
First, expand the parentheses on both sides:

\[
9(k - 4) = 9k - 36
\]
\[
-2(k + 8) = -2k - 16
\]

Now the equation becomes:

\[
9k - 36 - 7k = 32 - 2k - 16
\]

### Step 2: Simplify both sides
Combine like terms:

\[
(9k - 7k) - 36 = (32 - 16) - 2k
\]
\[
2k - 36 = 16 - 2k
\]

### Step 3: Move all terms involving \( k \) to one side and constants to the other side
Add \( 2k \) to both sides:

\[
2k + 2k - 36 = 16
\]
\[
4k - 36 = 16
\]

### Step 4: Solve for \( k \)
Add 36 to both sides:

\[
4k = 16 + 36
\]
\[
4k = 52
\]

Finally, divide by 4:

\[
k = \frac{52}{4} = 13
\]

### Final answer:
\[
k = 13
\]

Would you like further details on any step or have any questions?

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Here are 5 related questions to expand on this concept:
1. How do you solve an equation with fractions instead of whole numbers?
2. What happens if there are variables on both sides of the equation?
3. How do you check if the solution to an equation is correct?
4. What is the difference between solving linear and quadratic equations?
5. Can we solve an equation with more than one variable?

**Tip:** Always double-check your solution by substituting the value of the variable back into the original equation.

Learn how to solve the linear equation 9(k-4) - 7k = 32 - 2(k+8) with a detailed step-by-step explanation. This problem involves key algebraic concepts, such as the distributive property, simplifying equations, and combining like terms. Suitable for students in Grades 8-10.

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