Which of the following defines the solution set for the system of inequalities given below ?
0 > 3x - 6
-4 < x

Options

A. x gt -4
B. x lt 2
C. `-4 lt x lt 18`
D. `-4 lt x lt 2`

Answer

To solve the system of inequalities given by:

1. \( 0 > 3x - 6 \)
2. \( -4 < x \)

we will break down each inequality step by step.

### Step 1: Solve the first inequality
The first inequality is:
\[ 0 > 3x - 6 \]

We can rearrange this to:
\[ 3x - 6 < 0 \]

Next, we add 6 to both sides:
\[ 3x < 6 \]

Now, we divide both sides by 3:
\[ x < \frac{6}{3} \]

This simplifies to:
\[ x < 2 \]

### Step 2: Solve the second inequality
The second inequality is:
\[ -4 < x \]

This can be rewritten as:
\[ x > -4 \]

### Step 3: Combine the results
Now we have two inequalities:
1. \( x < 2 \)
2. \( x > -4 \)

To find the solution set that satisfies both inequalities, we combine them:
\[ -4 < x < 2 \]

### Final Solution
Thus, the solution set for the system of inequalities is:
\[ x > -4 \text{ and } x < 2 \]

This can be expressed as:
\[ -4 < x < 2 \]

### Conclusion
The correct option that defines the solution set for the system of inequalities is:
\[ x > -4 \text{ and } x < 2 \]