We need to solve the inequality:

\[
2(k - 3) > 6 + 3k - 3
\]

### Step 1: Expand the left-hand side
Expand the expression on the left-hand side:

\[
2(k - 3) = 2k - 6
\]

Now, the inequality becomes:

\[
2k - 6 > 6 + 3k - 3
\]

### Step 2: Simplify the right-hand side
Simplify the right-hand side:

\[
6 + 3k - 3 = 3 + 3k
\]

So, the inequality now is:

\[
2k - 6 > 3 + 3k
\]

### Step 3: Move terms involving \(k\) to one side
To isolate \(k\), subtract \(2k\) from both sides:

\[
-6 > 3 + k
\]

### Step 4: Isolate \(k\)
Now, subtract 3 from both sides:

\[
-9 > k
\]

This can also be written as:

\[
k < -9
\]

### Final Answer:
The solution is:

\[
k < -9
\]

Would you like more details or further explanation?

Here are 5 related questions to expand on this topic:
1. How do you solve inequalities that involve fractions?
2. What is the difference between solving equations and inequalities?
3. Can inequalities be graphed, and how does that help visualize solutions?
4. How do you handle inequalities when multiplying or dividing by a negative number?
5. What are some common mistakes to avoid when solving inequalities?

**Tip**: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Learn how to solve the inequality 2(k-3) > 6 + 3k - 3 through a step-by-step explanation. This solution covers essential algebraic concepts such as inequality manipulation and the distributive property. Ideal for students in Grades 7-9 looking to strengthen their understanding of linear inequalities.

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