Let's solve the equation:

\[
\frac{1}{4}k = 3\left(-\frac{1}{4}k + 3\right)
\]

### Step 1: Distribute the 3 on the right-hand side.

\[
\frac{1}{4}k = 3\left(-\frac{1}{4}k\right) + 3(3)
\]

This simplifies to:

\[
\frac{1}{4}k = -\frac{3}{4}k + 9
\]

### Step 2: Move all terms involving \(k\) to one side of the equation.

Add \(\frac{3}{4}k\) to both sides:

\[
\frac{1}{4}k + \frac{3}{4}k = 9
\]

### Step 3: Simplify the left-hand side.

\[
\frac{1}{4}k + \frac{3}{4}k = \frac{4}{4}k = k
\]

So, we have:

\[
k = 9
\]

Thus, the solution is:

\[
k = 9
\]

Do you want more details or have any questions?

Here are 5 related questions you could explore:
1. How do you handle equations with fractions in general?
2. What happens if there are multiple variables in the equation?
3. How can you check if your solution to an equation is correct?
4. What are some common mistakes when distributing terms in equations?
5. Can equations like this be solved graphically, and how would the graph look?

**Tip:** Always combine like terms on one side of the equation first to make solving simpler!

\dfrac{1}{4}k = 3\left(-\dfrac{1}{4}k + 3\right)

This page walks through solving the linear equation with fractions \dfrac{1}{4}k = 3(-\dfrac{1}{4}k + 3), including steps on distribution, combining like terms, and isolating the variable. Great for students in Grades 8-10 looking to enhance their algebra skills.

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