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Let's solve the equation step by step:

The given equation is:

\[
\frac{3}{4}k - 3 = -2k + \frac{3}{2}\left( 2 - \frac{2}{3}k \right)
\]

### Step 1: Distribute the \(\frac{3}{2}\) on the right-hand side
We first expand the right-hand side:

\[
\frac{3}{2}\left(2 - \frac{2}{3}k\right) = \frac{3}{2} \times 2 - \frac{3}{2} \times \frac{2}{3}k
\]

This simplifies to:

\[
\frac{3}{2} \times 2 = 3, \quad \frac{3}{2} \times \frac{2}{3} = 1
\]

So, the equation becomes:

\[
\frac{3}{4}k - 3 = -2k + 3 - k
\]

### Step 2: Combine like terms on the right-hand side
We combine \(-2k\) and \(-k\) on the right-hand side:

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

### Step 3: Move all terms involving \(k\) to one side
Add \(3k\) to both sides to bring all \(k\) terms together:

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

### Step 4: Combine the \(k\) terms on the left-hand side
We express \(3k\) with a denominator of 4, so:

\[
3k = \frac{12}{4}k
\]

Now the equation becomes:

\[
\frac{3}{4}k + \frac{12}{4}k - 3 = 3
\]

Combine the fractions:

\[
\frac{15}{4}k - 3 = 3
\]

### Step 5: Isolate \(k\)
Add 3 to both sides:

\[
\frac{15}{4}k = 6
\]

Multiply both sides by \(\frac{4}{15}\):

\[
k = \frac{6 \times 4}{15} = \frac{24}{15} = \frac{8}{5}
\]

### Final Answer:
\[
k = \frac{8}{5}
\]

Would you like further details or have any questions?

---

Here are five related questions to expand your understanding:
1. How would the process change if the constant on the right-hand side was negative?
2. What happens if the coefficients of \(k\) have different denominators?
3. How do we solve an equation with decimals instead of fractions?
4. Can you solve a similar equation using substitution?
5. How would the solution change if we had another variable involved?

**Tip**: When solving equations with fractions, it's often helpful to clear the denominators early on by multiplying through by the least common denominator (LCD).

Solve for k: (3/4)k - 3 = -2k + (3/2)(2 - (2/3)k)

Learn how to solve the equation (3/4)k - 3 = -2k + (3/2)(2 - (2/3)k) step-by-step using algebraic methods like distributing, combining like terms, and isolating variables. This detailed guide is perfect for students in Grades 8-10.

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