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Let's analyze the given expression and options. We are asked to find all expressions equivalent to:

\[
\frac{-6x - 4}{2}
\]

### Step 1: Simplify the given expression
We can simplify the expression by dividing both terms in the numerator by 2:

\[
\frac{-6x - 4}{2} = \frac{-6x}{2} + \frac{-4}{2} = -3x - 2
\]

So the simplified expression is \( -3x - 2 \).

### Step 2: Analyze the options

- **Option A: \( -3x - 2 \)**  
  This is exactly the simplified form, so **Option A** is correct.
  
- **Option B: \( 3x + 2 \)**  
  This is not equivalent to \( -3x - 2 \), so **Option B** is incorrect.
  
- **Option C: \( \frac{6x + 4}{2} \)**  
  Simplifying this expression gives:
  \[
  \frac{6x + 4}{2} = 3x + 2
  \]
  This is equivalent to Option B, which is incorrect, so **Option C** is also incorrect.

- **Option D: \( \frac{1}{2}(6x + 4) \)**  
  Simplifying this expression:
  \[
  \frac{1}{2}(6x + 4) = 3x + 2
  \]
  This is equivalent to \( 3x + 2 \), so **Option D** is incorrect.

- **Option E: \( \frac{1}{2}(-3x - 2) \)**  
  Simplifying this expression:
  \[
  \frac{1}{2}(-3x - 2) = -\frac{3x}{2} - 1
  \]
  This is not equivalent to \( -3x - 2 \), so **Option E** is incorrect.

### Conclusion:
The only correct answer is **Option A**.

---

Would you like more details on any of the steps? Here are some follow-up questions:

1. How do you distribute a fraction over an expression in parentheses?
2. Why isn't \( \frac{1}{2}(-3x - 2) \) equivalent to \( -3x - 2 \)?
3. How can you check if two expressions are equivalent?
4. What other methods can be used to simplify algebraic fractions?
5. How does factoring affect the equivalence of algebraic expressions?

**Tip:** Always simplify both the numerator and denominator separately before dividing when simplifying fractions.

Select all the expressions that are equivalent to (-6x - 4) / 2.

Learn how to simplify the expression (-6x - 4) / 2 and identify equivalent algebraic expressions. This problem explores core algebra concepts like the distributive property and fraction simplification, suitable for students in Grades 8-10.

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