https://file.aiquickdraw.com/mathbot/file/1729143608351y3x31sxi.jpg

The problem provided in the image can be translated from Indonesian as follows:

**"Solve the inequality \( 2 - (p - 4) \geq 2p + 12 \), where \( p \in \mathbb{B} \). Then, find the value of \( 2p \)."**

Let's solve this step by step:

1. **Expand the left-hand side:**
   \[
   2 - p + 4 \geq 2p + 12
   \]
   This simplifies to:
   \[
   6 - p \geq 2p + 12
   \]

2. **Move the terms involving \( p \) to one side and the constants to the other:**
   \[
   6 - 12 \geq 2p + p
   \]
   \[
   -6 \geq 3p
   \]

3. **Divide by 3 to solve for \( p \):**
   \[
   p \leq -2
   \]

Thus, \( p \leq -2 \).

To find the value of \( 2p \), we can use the smallest integer value of \( p \) that satisfies this inequality. Since \( p \in \mathbb{B} \) (assuming \( \mathbb{B} \) represents the set of integers), we take \( p = -2 \).

4. **Calculate \( 2p \):**
   \[
   2p = 2(-2) = -4
   \]

The value of \( 2p \) is \(-4\).

Would you like more details on any step, or do you have further questions?

Here are some related questions to expand your understanding:
1. How would the solution change if the inequality were \( 2 - (p - 4) > 2p + 12 \)?
2. What are the steps for solving inequalities with absolute values?
3. How do you solve a quadratic inequality?
4. What happens if \( \mathbb{B} \) represents real numbers instead of integers in this problem?
5. Can you represent this solution graphically on a number line?

**Tip:** When solving inequalities, remember to reverse the inequality sign if you multiply or divide by a negative number.

Solve the inequality 2 - (p - 4) ≥ 2p + 12, where p ∈ B. Then, find the value of 2p.

Learn how to solve the linear inequality 2 - (p - 4) ≥ 2p + 12. This problem involves algebraic manipulation and finding the value of 2p, suited for high school students in Grades 10-12.

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