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To solve for \( K \) in the equation:

\[
9 + 0.4K = K
\]

we can rearrange it as follows:

1. Move all terms involving \( K \) to one side of the equation. Subtract \( 0.4K \) from both sides:

   \[
   9 = K - 0.4K
   \]

2. Simplify the right side by factoring out \( K \):

   \[
   9 = (1 - 0.4)K
   \]

   \[
   9 = 0.6K
   \]

3. Divide both sides by \( 0.6 \) to isolate \( K \):

   \[
   K = \frac{9}{0.6}
   \]

4. Calculate the division:

   \[
   K = 15
   \]

So, the solution is:

\[
K = 15
\]

Would you like further details or have any questions?

Here are some related questions for further exploration:
1. What happens if we change the constant 9 in this equation to another number?
2. How would the solution change if the coefficient of \( K \) were different, say \( 0.5 \) instead of \( 0.4 \)?
3. How can we verify the solution for \( K \) by substituting it back into the original equation?
4. What is the general method for solving equations of the form \( a + bK = K \)?
5. How would the solution process change if \( K \) were a negative number?

**Tip:** In equations where \( K \) is on both sides, it’s usually helpful to combine like terms involving \( K \) to simplify the solving process.

Learn how to solve the linear equation 9 + 0.4K = K by isolating the variable K. This problem is ideal for students in Grades 7-9, focusing on algebraic rearrangement and basic linear equation solving techniques.

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