If n and s are integers, and `n+5lt7 and s-6lt-4`, which of the following could be a value of n+s?

Options

A. `2`
B. `5`
C. `4`
D. `6`

Answer

To solve the problem step by step, we will analyze the inequalities given and find the possible values of \( n + s \).

### Step 1: Analyze the first inequality
The first inequality given is:
\[ n + 5 < 7 \]

To isolate \( n \), we subtract 5 from both sides:
\[ n < 7 - 5 \]
\[ n < 2 \]

### Step 2: Analyze the second inequality
The second inequality given is:
\[ s - 6 < -4 \]

To isolate \( s \), we add 6 to both sides:
\[ s < -4 + 6 \]
\[ s < 2 \]

### Step 3: Combine the inequalities
Now we have:
1. \( n < 2 \) (from Step 1)
2. \( s < 2 \) (from Step 2)

We want to find the possible values of \( n + s \).

### Step 4: Determine the maximum value of \( n + s \)
Since both \( n \) and \( s \) are less than 2, we can express this as:
\[ n + s < 2 + 2 \]
\[ n + s < 4 \]

### Step 5: Check the options
Now we need to check which of the provided options could be a value of \( n + s \):
- Option A: 2
- Option B: 4
- Option C: (not provided in the question)
- Option D: 6

From our calculation, we know that \( n + s < 4 \). Therefore:
- Option A (2) is valid because \( 2 < 4 \).
- Option B (4) is not valid because \( 4 \) is not less than \( 4 \).
- Option D (6) is also not valid because \( 6 > 4 \).

Thus, the only possible value for \( n + s \) from the options given is:
**2**