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Let's analyze the provided questions step by step.

### Equations:
- **A:** \( \frac{x}{4} + 1 = -3 \)
- **B:** \( x + 4 = -12 \)

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### Question 1: **How can we get Equation B from Equation A?**
We start with Equation A:
\[ \frac{x}{4} + 1 = -3 \]

1. **Eliminate the fraction by multiplying through by 4**:
   \[
   4 \cdot \left(\frac{x}{4}\right) + 4 \cdot 1 = 4 \cdot (-3)
   \]
   This simplifies to:
   \[
   x + 4 = -12
   \]
   Now, Equation B is derived.

   **Correct Answer:** **D - Multiply/divide both sides by the same non-zero constant.**

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### Question 2: **Are the equations equivalent?**
Since we derived Equation B directly from Equation A by multiplying both sides by 4 (a valid algebraic operation), the two equations are equivalent and share the same solution.

   **Correct Answer:** **A - Yes.**

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Would you like more explanation on any of the steps?  

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### 5 Related Questions:
1. What are the algebraic rules for maintaining equivalence between equations?  
2. Can fractions always be cleared by multiplying both sides?  
3. How can solutions of linear equations be verified?  
4. What happens if only one side of an equation is multiplied by a constant?  
5. How does combining like terms differ from multiplication/division?  

### Tip:
Always perform the same operation on both sides of an equation to maintain equivalence.

Answer two questions about Equations A and B:
1) How can we get Equation B from Equation A?
2) Based on the previous answer, are the equations equivalent?

Learn how to derive one linear equation from another and check for equivalence. This step-by-step solution explores algebraic techniques such as eliminating fractions and validating solutions. Perfect for Grades 8-10.

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