If `-3lt2x+4lt9`, which of the following CANNOT be a possible value of x?

Options

A. `-2`
B. `-4`
C. `0`
D. `2`

Answer

To solve the inequality \(-3 < 2x + 4 < 9\), we will break it down step by step.

### Step 1: Split the inequality
We can separate the compound inequality into two parts:
\[ -3 < 2x + 4 \quad \text{and} \quad 2x + 4 < 9 \]

### Step 2: Solve the first part
Let's solve the first part of the inequality:
\[ -3 < 2x + 4 \]
Subtract 4 from both sides:
\[ -3 - 4 < 2x \]
This simplifies to:
\[ -7 < 2x \]
Now, divide both sides by 2:
\[ -\frac{7}{2} < x \]
This can also be written as:
\[ x > -3.5 \]

### Step 3: Solve the second part
Now, let's solve the second part of the inequality:
\[ 2x + 4 < 9 \]
Subtract 4 from both sides:
\[ 2x < 9 - 4 \]
This simplifies to:
\[ 2x < 5 \]
Now, divide both sides by 2:
\[ x < \frac{5}{2} \]
This can also be written as:
\[ x < 2.5 \]

### Step 4: Combine the results
Now we can combine the results from both parts:
\[ -3.5 < x < 2.5 \]

### Step 5: Identify the values
This means that \(x\) can take any value between \(-3.5\) and \(2.5\). To find which of the given options cannot be a possible value of \(x\), we check the options against this interval.

### Conclusion
The values that cannot be possible for \(x\) are those that lie outside the interval \((-3.5, 2.5)\). For example, if one of the options is \(-4\), it cannot be a possible value of \(x\) since \(-4 < -3.5\).