If `3-(3)/(x)=x+7` and xne0`, which of the following is a possible value for x?

Options

A. `-7`
B. `-1`
C. `1`
D. `3`

Answer

To solve the equation \( 3 - \frac{3}{x} = x + 7 \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the original equation:
\[ 3 - \frac{3}{x} = x + 7 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply every term by \( x \) (noting that \( x \neq 0 \)):
\[ 3x - 3 = x^2 + 7x \]

### Step 3: Rearrange the equation
Rearranging the equation gives:
\[ 3x - 3 - x^2 - 7x = 0 \]
This simplifies to:
\[ -x^2 - 4x - 3 = 0 \]
Multiplying through by -1 to make the leading coefficient positive:
\[ x^2 + 4x + 3 = 0 \]

### Step 4: Factor the quadratic equation
Now, we can factor the quadratic:
\[ (x + 1)(x + 3) = 0 \]

### Step 5: Solve for x
Setting each factor to zero gives:
\[ x + 1 = 0 \quad \text{or} \quad x + 3 = 0 \]
Thus, we find:
\[ x = -1 \quad \text{or} \quad x = -3 \]

### Step 6: Identify possible values
Since the question asks for a possible value of \( x \), we have two possible values: \( x = -1 \) and \( x = -3 \). However, if we look for the value that is specifically mentioned in the options, we note that \( -1 \) is a possible value.

### Final Answer
The possible value for \( x \) is:
\[ \boxed{-1} \]