If `3b+8gt6+2b`, and b is a negative integer, what is the value of b?

Options

A. `0`
B. `-1`
C. `-2`
D. `-3`

Answer

To solve the inequality \(3b + 8 > 6 + 2b\) and find the value of \(b\) given that \(b\) is a negative integer, we can follow these steps:

### Step 1: Rearranging the Inequality
Start with the original inequality:
\[ 3b + 8 > 6 + 2b \]

### Step 2: Move all terms involving \(b\) to one side
Subtract \(2b\) from both sides:
\[ 3b - 2b + 8 > 6 \]
This simplifies to:
\[ b + 8 > 6 \]

### Step 3: Move constant terms to the other side
Subtract \(8\) from both sides:
\[ b > 6 - 8 \]
This simplifies to:
\[ b > -2 \]

### Step 4: Identify possible values for \(b\)
Since \(b\) is a negative integer, the values that satisfy \(b > -2\) and are negative integers are:
- \(b = -1\)

### Conclusion
Thus, the only negative integer value that satisfies the inequality is:
\[ b = -1 \]

### Final Answer
The value of \(b\) is \(-1\).

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