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The question is asking for the inequality that represents "twelve times the sum of three plus \( c \) is greater than 27."

Let's break down the statement:

1. **Twelve times the sum of three plus \( c \):**
   - The "sum of three plus \( c \)" can be written as \( 3 + c \).
   - "Twelve times" this sum would be \( 12 \times (3 + c) \).

2. **Is greater than 27:**
   - This means we want to set up an inequality where the expression above is greater than 27.

Combining these parts, the correct inequality is:

\[
12 \times (3 + c) > 27
\]

Now let's identify this option from the provided choices:

- **Option A: \( 12 (3 + c) > 27 \)** — This matches the expression we derived.
- **Options B to E:** None of these represent "twelve times the sum of three plus \( c \) is greater than 27."

Therefore, the correct answer is:

**A. \( 12 (3 + c) > 27 \)**

Would you like a detailed explanation of why the other options are incorrect or have any other questions?

### Related Questions:

1. How do you solve an inequality like \( 12(3 + c) > 27 \) for \( c \)?
2. What are the properties of inequalities that are important to remember?
3. How would the inequality change if it was "less than" instead of "greater than"?
4. Can you provide an example of a word problem that leads to a similar inequality?
5. How does distributing multiplication over addition work in algebra?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Which inequality shows twelve times the sum of three plus c is greater than 27?

Learn how to solve the inequality where twelve times the sum of 3 plus c is greater than 27. This problem covers essential algebra concepts, including inequalities and the distributive property. Suitable for students in Grades 6-8.

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