**Solve for \[x\].**
*Assume the equation has a solution for \[x\].*

\[d\cdot(-3+x) = kx+9\]

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

\[
d \cdot (-3 + x) = kx + 9
\]

Start by distributing \(d\) on the left-hand side:

\[
d(-3) + dx = kx + 9
\]

This simplifies to:

\[
-3d + dx = kx + 9
\]

Next, move all terms involving \(x\) to one side of the equation and constants to the other side:

\[
dx - kx = 3d + 9
\]

Factor out \(x\) on the left side:

\[
x(d - k) = 3d + 9
\]

Finally, solve for \(x\) by dividing both sides by \((d - k)\):

\[
x = \frac{3d + 9}{d - k}
\]

This is the solution for \(x\).

Would you like more details or have any questions?

Here are some related questions:

1. What conditions must be met for the solution to be valid?
2. How does the equation change if \(d = 0\) or \(k = 0\)?
3. What does the solution look like if \(d = k\)?
4. How can you verify the solution by plugging it back into the original equation?
5. What happens to the solution as \(d\) or \(k\) approaches certain values?

**Tip:** Always check the denominator when solving for a variable to ensure it does not lead to division by zero.

Learn how to solve the equation d*(-3+x) = kx+9 step-by-step with a detailed solution. This problem involves linear equations and the distributive property. Suitable for students in Grades 9-12.

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