Solve for \[x\]. Assume the equation has a solution for \[x\]. \[d\cdot(-3+x) = kx+9\] use an asterisk for the solution

To solve the equation for \(x\):

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

Let's distribute \(d\) on the left side:

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

This simplifies to:

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

Now, let's move all the terms involving \(x\) to one side and the constants to the other:

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

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

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

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

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

The solution for \(x\) is:

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

Would you like more details or have any questions?

Here are some related questions:

1. What happens if \(d = k\)? 
2. How does the solution change if \(d\) or \(k\) is negative?
3. What is the significance of the constant term in the equation?
4. How would you solve the equation if additional terms were present?
5. Can you factor out common terms in the numerator?

**Tip:** Always check if any term simplifies or cancels out before solving for the variable to make the process more efficient.

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 Grades 7-9.

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