The value of m, if the value of `3x^(2) + x - m` is equal to 7, when x = -1 is

Options

A. `-5`
B. 8
C. `-7`
D. 12

Answer

To find the value of \( m \) in the expression \( 3x^2 + x - m \) when \( x = -1 \) and the expression equals 7, we can follow these steps:

### Step 1: Substitute \( x = -1 \) into the expression
We start with the expression:
\[ 3x^2 + x - m \]
Substituting \( x = -1 \):
\[ 3(-1)^2 + (-1) - m \]

### Step 2: Calculate \( 3(-1)^2 \)
Calculating \( (-1)^2 \):
\[ (-1)^2 = 1 \]
So,
\[ 3(-1)^2 = 3 \times 1 = 3 \]

### Step 3: Substitute back into the expression
Now we substitute this back into the expression:
\[ 3 + (-1) - m \]
This simplifies to:
\[ 3 - 1 - m = 2 - m \]

### Step 4: Set the expression equal to 7
According to the problem, this expression equals 7:
\[ 2 - m = 7 \]

### Step 5: Solve for \( m \)
To find \( m \), we rearrange the equation:
\[ -m = 7 - 2 \]
\[ -m = 5 \]
Multiplying both sides by -1 gives:
\[ m = -5 \]

### Final Answer
Thus, the value of \( m \) is:
\[ \boxed{-5} \]