If `(x-3y)/(x)=7`, what is the value of `(x)/(y)`?

Options

A. `-(8)/(3)`
B. `-2`
C. `-(1)/(2)`
D. `(3)/(8)`

Explanation

To solve the equation \(\frac{x - 3y}{x} = 7\) and find the value of \(\frac{x}{y}\), we can follow these steps:

### Step 1: Start with the given equation
\[ \frac{x - 3y}{x} = 7 \]

### Step 2: Simplify the left side
We can rewrite the left side by separating the terms:
\[ \frac{x}{x} - \frac{3y}{x} = 7 \]
This simplifies to:
\[ 1 - \frac{3y}{x} = 7 \]

### Step 3: Isolate the term with \(y\)
Now, we will isolate \(\frac{3y}{x}\):
\[ -\frac{3y}{x} = 7 - 1 \]
This simplifies to:
\[ -\frac{3y}{x} = 6 \]

### Step 4: Multiply both sides by -1
To get rid of the negative sign, we multiply both sides by -1:
\[ \frac{3y}{x} = -6 \]

### Step 5: Solve for \(\frac{y}{x}\)
Now, we can divide both sides by 3:
\[ \frac{y}{x} = -2 \]

### Step 6: Find \(\frac{x}{y}\)
To find \(\frac{x}{y}\), we take the reciprocal of \(\frac{y}{x}\):
\[ \frac{x}{y} = -\frac{1}{2} \]

### Final Answer
Thus, the value of \(\frac{x}{y}\) is:
\[ \frac{x}{y} = -\frac{1}{2} \]

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