If (x - 3)(2x + 1) = 0, then the possible values of 2x + 1 are:

Options

A. 0 only
B. 0 and 3
C. `- 1/2`and 3
D. 0 and 7

Answer

To solve the equation \((x - 3)(2x + 1) = 0\) and find the possible values of \(2x + 1\), we can follow these steps:

### Step 1: Set each factor to zero
Since the product of two factors is zero, we can set each factor equal to zero:
1. \(x - 3 = 0\)
2. \(2x + 1 = 0\)

### Step 2: Solve the first equation
From the first equation:
\[ x - 3 = 0 \]
Adding 3 to both sides gives:
\[ x = 3 \]

### Step 3: Substitute \(x = 3\) into \(2x + 1\)
Now, we substitute \(x = 3\) into the expression \(2x + 1\):
\[ 2(3) + 1 = 6 + 1 = 7 \]

### Step 4: Solve the second equation
Now, we solve the second equation:
\[ 2x + 1 = 0 \]
Subtracting 1 from both sides gives:
\[ 2x = -1 \]
Dividing both sides by 2 gives:
\[ x = -\frac{1}{2} \]

### Step 5: Substitute \(x = -\frac{1}{2}\) into \(2x + 1\)
Next, we substitute \(x = -\frac{1}{2}\) into the expression \(2x + 1\):
\[ 2\left(-\frac{1}{2}\right) + 1 = -1 + 1 = 0 \]

### Conclusion
The possible values of \(2x + 1\) are:
- When \(x = 3\), \(2x + 1 = 7\)
- When \(x = -\frac{1}{2}\), \(2x + 1 = 0\)

Thus, the possible values of \(2x + 1\) are **0 and 7**.