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The problem asks to find the solution set (\( HP \)) for the inequality:

\[
3(x - 2) \leq 2x
\]

Let’s solve the inequality step by step:

### Step 1: Expand and simplify
\[
3(x - 2) \leq 2x
\]
\[
3x - 6 \leq 2x
\]

### Step 2: Rearrange terms
\[
3x - 2x \leq 6
\]
\[
x \leq 6
\]

This means that the solution set includes all \( x \) values less than or equal to 6.

### Step 3: Consider the options
Since \( x \) must be a member of set \( A \), and we have \( x \leq 6 \), we must check each option given:

- **A**: \( \{1, 2, 3, 4, 5, 6\} \) — All values are \( \leq 6 \). This is a valid solution set.
- **B**: \( \{1, 2, 3, 4, 5\} \) — This does not include 6, so it is not complete.
- **C**: \( \{0, 1, 2, 3, 4, 5, 6\} \) — This includes 0, which is valid since 0 is also \( \leq 6 \).
- **D**: \( \{0, 1, 2, 3, 4, 5\} \) — This does not include 6, so it is not complete.

### Step 4: Choose the correct option
The most accurate and complete set that satisfies \( x \leq 6 \) is **Option C**, which includes all possible values \( x \) can take within that range, including 0 and 6.

Thus, the correct answer is:
\[
\textbf{C. HP = \{0, 1, 2, 3, 4, 5, 6\}}
\]

Would you like further details or explanations on this solution?

### Additional Questions:
1. How do you solve inequalities involving multiplication or division by negative numbers?
2. What happens if we change the inequality sign to \( > \) instead of \( \leq \)?
3. How do you represent the solution of an inequality on a number line?
4. What is the difference between a strict inequality (\( < \) or \( > \)) and a non-strict inequality (\( \leq \) or \( \geq \))?
5. How do you check if a particular value is a solution to a given inequality?

### Tip:
Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number!

Himpunan penyelesaian dari 3(x - 2) ≤ 2x, untuk x ∈ A adalah ....

Find the solution set for the inequality 3(x - 2) ≤ 2x. This problem involves solving a linear inequality step-by-step and analyzing the solution with given options. Suitable for students in Grades 7-9.

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