At a store each notebook has a cost of x dollars. Which situation can be represented by this inequality?
 
6x < 2x + 3
A.The cost of 6 notebooks is greater than the cost of 2 notebooks plus a $3 pen.
B.The cost of 6 notebooks is less than the cost of 2 notebooks with a $3-off coupon.
C.The cost of 6 notebooks is less than the cost of 2 notebooks plus a $3 pen.
D.The cost of 6 notebooks is $3 greater than the than the price of 2 notebooks.

Let's analyze the inequality step by step: 

The inequality is:

\[
6x < 2x + 3
\]

- On the left-hand side, we have the cost of 6 notebooks: $6x$.
- On the right-hand side, we have the cost of 2 notebooks: $2x$, plus an additional $3.

This means the left side (the cost of 6 notebooks) is less than the right side (the cost of 2 notebooks plus $3). 

Now, let's review the options:
- **Option A**: The cost of 6 notebooks is greater than the cost of 2 notebooks plus a $3 pen.  
  This doesn't match, since the inequality says "less than" not "greater than".
  
- **Option B**: The cost of 6 notebooks is less than the cost of 2 notebooks with a $3-off coupon.  
  This would subtract $3 from the right side, but the inequality adds $3 to the right side.

- **Option C**: The cost of 6 notebooks is less than the cost of 2 notebooks plus a $3 pen.  
  This matches the structure of the inequality.

- **Option D**: The cost of 6 notebooks is $3 greater than the price of 2 notebooks.  
  This would suggest $6x = 2x + 3$, but the inequality specifies "less than."

Thus, the correct answer is:

**C. The cost of 6 notebooks is less than the cost of 2 notebooks plus a $3 pen.**

Would you like a detailed breakdown of solving this inequality?

Here are 5 related questions to consider:
1. How would the inequality change if the cost of a pen were subtracted instead of added?
2. How can you solve for $x$ in the inequality $6x < 2x + 3$?
3. What happens if the number of notebooks on both sides of the inequality changes?
4. What is the interpretation of the inequality if the inequality sign changes from "<" to ">"?
5. How would this problem change if the cost of a pen is represented by another variable, say $y$?

**Tip**: When dealing with inequalities, remember that the inequality sign reverses if you multiply or divide by a negative number.

At a store each notebook has a cost of x dollars. Which situation can be represented by this inequality? 6x < 2x + 3 A. The cost of 6 notebooks is greater than the cost of 2 notebooks plus a $3 pen. B. The cost of 6 notebooks is less than the cost of 2 notebooks with a $3-off coupon. C. The cost of 6 notebooks is less than the cost of 2 notebooks plus a $3 pen. D. The cost of 6 notebooks is $3 greater than the than the price of 2 notebooks.

Understand how to solve the linear inequality 6x < 2x + 3 by comparing the cost of 6 notebooks to the cost of 2 notebooks plus an additional $3 pen. This algebra problem explores key concepts of linear inequalities and is suitable for students in Grades 6-8.

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