Which equation has the same solution as the equation 5 - 3(y + 4) = 14?
(12 - 3y) / 3 = -y + 7
y/2 + 3 = -4
-2(3 - y) = 2y + 1
5y + 7 = 4y

Let's solve the original equation step by step to find the value of \( y \):

### Original equation:  
\[
5 - 3(y + 4) = 14
\]

1. **Distribute** the -3 over the terms inside the parentheses:
\[
5 - 3y - 12 = 14
\]

2. **Simplify** the constants:
\[
-3y - 7 = 14
\]

3. **Add 7** to both sides to isolate the term with \( y \):
\[
-3y = 21
\]

4. **Divide** by -3 to solve for \( y \):
\[
y = -7
\]

### Now, let's check which of the given equations has the same solution \( y = -7 \).

#### 1. \(\frac{12 - 3y}{3} = -y + 7\)

Substitute \( y = -7 \):
\[
\frac{12 - 3(-7)}{3} = -(-7) + 7
\]
Simplifying both sides:
\[
\frac{12 + 21}{3} = 7 + 7
\]
\[
\frac{33}{3} = 14 \quad \text{and} \quad 14 = 14
\]
This equation is **true**, so it has the same solution as the original.

#### 2. \(\frac{y}{2} + 3 = -4\)

Substitute \( y = -7 \):
\[
\frac{-7}{2} + 3 = -4
\]
Simplifying:
\[
-3.5 + 3 = -4
\]
\[
-0.5 \neq -4
\]
This equation is **false**, so it does not have the same solution.

#### 3. \(-2(3 - y) = 2y + 1\)

Substitute \( y = -7 \):
\[
-2(3 - (-7)) = 2(-7) + 1
\]
Simplifying both sides:
\[
-2(3 + 7) = -14 + 1
\]
\[
-2(10) = -13
\]
\[
-20 \neq -13
\]
This equation is **false**, so it does not have the same solution.

#### 4. \(5y + 7 = 4y\)

Substitute \( y = -7 \):
\[
5(-7) + 7 = 4(-7)
\]
Simplifying both sides:
\[
-35 + 7 = -28
\]
\[
-28 = -28
\]
This equation is **true**, so it has the same solution.

### Conclusion:
The equations that have the same solution as the original are:

1. \(\frac{12 - 3y}{3} = -y + 7\)
2. \(5y + 7 = 4y\)

Would you like more details on any step?  
Here are some related questions for practice:

1. Solve the equation \( 4(2 - y) = 10y - 8 \).
2. Which equation has the same solution as \( 3y + 5 = 2

Learn how to solve the linear equation 5 - 3(y + 4) = 14 step by step and determine which of the given equations have the same solution. This problem demonstrates key algebraic concepts such as distribution, solving for variables, and equation comparison. Suitable for students in Grades 7-9.

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