If x is a negative integar , then the solution set of `-12x gt 30` is

Options

A. A. `{-2,-1}`
B. B. `{…,-5,-4,-3}`
C. C. `{…,-5,-4,-3,-2}`
D. D. `{-2,-1,0,1,2…}`

Answer

To solve the inequality \(-12x > 30\) given that \(x\) is a negative integer, we will follow these steps:

### Step 1: Rewrite the Inequality
We start with the inequality:
\[ -12x > 30 \]

### Step 2: Divide by -12
To isolate \(x\), we divide both sides of the inequality by \(-12\). Remember, when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign flips:
\[ x < \frac{30}{-12} \]

### Step 3: Simplify the Right Side
Now, we simplify \(\frac{30}{-12}\):
\[ \frac{30}{-12} = -\frac{30}{12} = -\frac{5}{2} \]
So, we have:
\[ x < -\frac{5}{2} \]

### Step 4: Convert to Decimal
Next, we can convert \(-\frac{5}{2}\) to a decimal:
\[ -\frac{5}{2} = -2.5 \]
Thus, we have:
\[ x < -2.5 \]

### Step 5: Identify Negative Integers
Since \(x\) must be a negative integer, we look for integers that are less than \(-2.5\). The negative integers less than \(-2.5\) are:
\[ -3, -4, -5, \ldots \]

### Step 6: Write the Solution Set
The solution set of negative integers satisfying the inequality is:
\[ \{ -3, -4, -5, \ldots \} \text{ or } (-\infty, -3] \]

### Conclusion
Thus, the correct answer is option B: \(-\infty, -5, -4, -3\).

---