Given the equation `6/x = (3)/(k +2)` and the constraints `x ne 0 and k ne -2,` what is x in terms of k ?

Options

A. `x =2k + 4`
B. `x =2k +12`
C. `x =2k -1/4`
D. `x =1/4 k +12`

Answer

To solve the equation \( \frac{6}{x} = \frac{3}{k + 2} \) for \( x \) in terms of \( k \), we can follow these steps:

### Step 1: Cross-multiply the equation
We start with the equation:
\[ \frac{6}{x} = \frac{3}{k + 2} \]
Cross-multiplying gives us:
\[ 6(k + 2) = 3x \]

### Step 2: Distribute on the left side
Now, we distribute \( 6 \) on the left side:
\[ 6k + 12 = 3x \]

### Step 3: Isolate \( x \)
Next, we want to isolate \( x \). We can do this by dividing both sides of the equation by \( 3 \):
\[ x = \frac{6k + 12}{3} \]

### Step 4: Simplify the expression
Now, we simplify the right side:
\[ x = 2k + 4 \]

### Final Answer
Thus, \( x \) in terms of \( k \) is:
\[ x = 2k + 4 \]