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

We are asked to determine which of the given equations has the same solution as the equation:  
\[
5 - 3(y + 4) = 14.
\]

---

### Step 1: Solve the original equation.

\[
5 - 3(y + 4) = 14.
\]
Expand the expression on the left side:

\[
5 - 3y - 12 = 14.
\]
Simplify:

\[
-3y - 7 = 14.
\]
Add 7 to both sides:

\[
-3y = 21.
\]
Divide by -3:

\[
y = -7.
\]

---

### Step 2: Check which equation has \(y = -7\) as a solution.

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

\[
\frac{12 - 3(-7)}{3} = -(-7) + 7.
\]

Simplify both sides:

\[
\frac{12 + 21}{3} = 7 + 7 \quad \Rightarrow \quad \frac{33}{3} = 14 \quad \Rightarrow \quad 11 \neq 14.
\]

This is not the correct equation.

---

#### 2. \(\frac{y}{2} + 3 = -4\)
Substitute \(y = -7\):

\[
\frac{-7}{2} + 3 = -4.
\]

Simplify:

\[
-3.5 + 3 = -0.5 \quad \neq -4.
\]

This is not the correct equation.

---

#### 3. \(-2(3 - y) = 2y + 1\)
Substitute \(y = -7\):

\[
-2(3 - (-7)) = 2(-7) + 1.
\]

Simplify both sides:

\[
-2(3 + 7) = -14 + 1 \quad \Rightarrow \quad -2(10) = -13 \quad \Rightarrow \quad -20 \neq -13.
\]

This is not the correct equation.

---

#### 4. \(5y + 7 = 4y\)
Substitute \(y = -7\):

\[
5(-7) + 7 = 4(-7).
\]

Simplify both sides:

\[
-35 + 7 = -28 \quad \Rightarrow \quad -28 = -28.
\]

This is the correct equation.

---

### Step 3: Final Answer
The equation that has the same solution as \(5 - 3(y + 4) = 14\) is:

\[
5y + 7 = 4y.
\]

---

Do you have any questions or need further details?  

Here are five related questions you might explore:  
1. How do you solve linear equations involving parentheses?  
2. How can you check if two equations have the same solution without solving both?  
3. What are equivalent equations?  
4. Can different forms of equations represent the same solution?  
5. How do you isolate variables in multi-step equations?  

**Tip:** Always substitute the solution back into the equation to verify your answer.

Which equation has the same solution as the equation 5 - 3(y + 4) = 14?

Discover how to solve the linear equation 5 - 3(y + 4) = 14 and determine which of the given equations has the same solution. This step-by-step solution covers important algebraic concepts such as expanding parentheses, isolating the variable, and verifying solutions. Suitable for Grades 8-10.

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