https://file.aiquickdraw.com/mathbot/file/1728918743985cz1umlpw.jpg

The question shown in the image is:

"Himpunan penyelesaian dari \( 3(x - 2) \leq 2x \), untuk \( x \in A \) adalah ...."

This is an inequality problem that asks for the solution set of the inequality \( 3(x - 2) \leq 2x \).

### Let's solve it step by step:

1. **Distribute** the \( 3 \) on the left-hand side:
   \[
   3(x - 2) = 3x - 6
   \]
   So the inequality becomes:
   \[
   3x - 6 \leq 2x
   \]

2. **Isolate the variable** \( x \):
   Subtract \( 2x \) from both sides:
   \[
   3x - 2x - 6 \leq 0
   \]
   Simplifying this gives:
   \[
   x - 6 \leq 0
   \]

3. **Solve for \( x \)**:
   Add 6 to both sides:
   \[
   x \leq 6
   \]

Thus, the solution set is \( x \leq 6 \), which means \( x \) can be any number less than or equal to 6.

### Final Answer:
The solution set for the inequality \( 3(x - 2) \leq 2x \) is \( x \leq 6 \).

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Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How would the solution change if the inequality were strict, i.e., \( 3(x - 2) < 2x \)?
2. What would the graph of this solution look like on a number line?
3. Can you solve a system of inequalities, such as \( 3(x - 2) \leq 2x \) and \( x + 4 \geq 2x \)?
4. How can we express this solution using set notation?
5. How do you solve an inequality that involves fractions, such as \( \frac{1}{x - 2} \leq 2x \)?

**Tip:** Always check if reversing an inequality sign is necessary when multiplying or dividing by a negative number during the solution process.

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

This article covers how to solve the inequality 3(x - 2) <= 2x. Learn the step-by-step method to simplify the inequality and find the solution set for x. Suitable for students in Grades 7-9.

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