Final answer:
After solving the inequality 4 > 3n + 1 > -8 for n, we find that the possible values of n are in the range -3 < n < 1. Thus, the correct option is b) -2, which falls within this range.
Step-by-step explanation:
To find the possible value of n in the inequality 4 > 3n + 1 > -8, we need to solve for n separately in both parts of the inequality.
First, let's solve the right-hand side of the inequality: 3n + 1 > -8. Subtract 1 from both sides to get 3n > -9. Then, divide both sides by 3 to get n > -3. This gives us one part of our solution: n must be greater than -3.
Now, let's solve the left-hand side of the inequality: 4 > 3n + 1. Subtract 1 from both sides to get 3 > 3n. Then, divide both sides by 3 to get 1 > n or n < 1. This provides the second part of our solution.
So, combining both parts, we get -3 < n < 1. Looking at the options provided:
- a) -3: This is not a possible value since n must be greater than -3.
- b) -2: This is a possible value since -2 is between -3 and 1.
- c) n > -3: This is true, but it is not a value; it's a range.
- d) n < 2: While true, -2 is still a more precise answer within the range given.
Therefore, the correct option is b) -2.