The sum of a number and six is seven times the number.

n − 6 = 7 n

*n* + 6 = 7*n*

n = 7 n + 6

7(*n* + 6) = *n*

Given the sentence "The sum of a number and six is seven times the number," let's analyze the options provided:

1. **\( n - 6 = 7n \)**:
   - This equation reads as "the difference of a number and six is seven times the number," which doesn't match the problem statement.

2. **\( n + 6 = 7n \)**:
   - This correctly translates to "the sum of a number and six is seven times the number."

3. **\( n = 7n + 6 \)**:
   - This reads as "a number is equal to seven times the number plus six," which is different from the problem statement.

4. **\( 7(n + 6) = n \)**:
   - This reads as "seven times the sum of a number and six is the number," which doesn't match the problem statement.

The correct translation of the sentence into an equation is:

\[
\boxed{n + 6 = 7n}
\]

Would you like to see how this equation can be solved or have any other questions?

Here are some related questions:
1. How do you solve the equation \( n + 6 = 7n \)?
2. Why is it important to match the order of operations in word problems when forming equations?
3. What are common mistakes when translating word problems into equations?
4. How would you write an equation for "Three more than twice a number is ten"?
5. What strategies can help in identifying the correct equation form in word problems?

**Tip:** Always ensure the equation reflects the exact relationship described in the word problem by carefully matching terms and operations.

Explore how to solve the problem 'The sum of a number and six is seven times the number'. This problem involves translating a verbal statement into a mathematical equation and solving it step-by-step. Suitable for students in Grades 6-8.

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