Let's answer the given questions step-by-step.
### Given Equations:
- Equation A: [tex]\(\frac{x}{4} + 1 = -3\)[/tex]
- Equation B: [tex]\(x + 4 = -12\)[/tex]
### Question 1: How can we get Equation B from Equation A?
Let's solve Equation A for [tex]\(x\)[/tex] and see if we can transform it into Equation B.
#### Step-by-Step Solution for Equation A:
1. Start with Equation A:
[tex]\[
\frac{x}{4} + 1 = -3
\][/tex]
2. Subtract 1 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
\frac{x}{4} = -3 - 1
\][/tex]
[tex]\[
\frac{x}{4} = -4
\][/tex]
3. Multiply both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = -4 \times 4
\][/tex]
[tex]\[
x = -16
\][/tex]
Now that we have [tex]\(x = -16\)[/tex], let's substitute [tex]\(x\)[/tex] into Equation B to check if we get the same equation.
4. Substitute [tex]\(x = -16\)[/tex] into Equation B:
[tex]\[
x + 4 = -12
\][/tex]
[tex]\[
-16 + 4 = -12
\][/tex]
[tex]\[
-12 = -12
\][/tex]
This shows that the value of [tex]\(x\)[/tex] from Equation A satisfies Equation B.
### Choosing the Transformation Method:
From the solving process, it is clear that:
- We multiplied both sides of Equation A by a constant (non-zero) value. This means the correct method is:
[tex]\[
\boxed{\text{D) Multiply/divide both sides by the same nonzero constant}}
\][/tex]
### Question 2: Are the equations equivalent?
Based on the transformation method chosen above and the calculations, we verified that:
- The value [tex]\(x = -16\)[/tex] obtained from Equation A satisfies Equation B.
- Both equations, after proper manipulation, result in the same [tex]\(x\)[/tex] value and maintain equality when simplifying properly.
Therefore, the equations are indeed equivalent.
[tex]\[
\boxed{\text{Yes, the equations are equivalent.}}
\][/tex]
