https://file.aiquickdraw.com/mathbot/file/1727417910035z34rpue6.jpg

Tentukan Himpunan Penyelesaian (HP) untuk setiap pertidaksamaan pada sistem bilangan real

The inequality given in the image is:

\[
2 - 3x \leq 12
\]

We will solve it step by step:

### Step 1: Isolate the term with \( x \)
Subtract 2 from both sides:
\[
-3x \leq 12 - 2
\]
\[
-3x \leq 10
\]

### Step 2: Solve for \( x \)
Now, divide both sides by \( -3 \). Remember, when dividing or multiplying by a negative number, the inequality sign must be flipped:
\[
x \geq \frac{10}{-3}
\]
\[
x \geq -\frac{10}{3}
\]

### Conclusion:
The solution set for the inequality is:
\[
x \geq -\frac{10}{3}
\]
This means the values of \( x \) are all real numbers greater than or equal to \( -\frac{10}{3} \).

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Would you like further details or clarifications?

Here are some related questions for further exploration:
1. How do we handle inequalities involving multiplication or division by negative numbers?
2. What is the interval notation for this solution set?
3. How would the solution change if the inequality was strict (\( < \) or \( > \))?
4. What would be the solution if the coefficient of \( x \) were positive?
5. Can we represent the solution graphically on a number line?

**Tip:** When solving inequalities, always be mindful of flipping the inequality sign when multiplying or dividing by a negative value!

Tentukan Himpunan Penyelesaian (HP) untuk setiap pertidaksamaan berikut: 2 - 3x ≤ 12

Learn how to solve the linear inequality 2 - 3x ≤ 12 with detailed steps. This problem demonstrates key concepts of algebra, including manipulating inequalities and flipping the inequality sign when dividing by negative numbers. Ideal for students in Grades 7-9.

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