https://file.aiquickdraw.com/mathbot/file/17272075958056lw4rxcn.jpg

The given equation is:

\[
\frac{y - 2x}{x} = \frac{y}{3}
\]

We are asked to solve for \(x\). Let's solve it step by step.

### Step 1: Multiply both sides by \(x\)
This eliminates the denominator on the left-hand side:

\[
y - 2x = \frac{y}{3} \cdot x
\]

### Step 2: Distribute \(\frac{y}{3}\) on the right-hand side:

\[
y - 2x = \frac{yx}{3}
\]

### Step 3: Get all terms involving \(x\) on one side
Move the \(\frac{yx}{3}\) term to the left side:

\[
y - 2x - \frac{yx}{3} = 0
\]

### Step 4: Combine the terms involving \(x\)
Multiply the equation by 3 to eliminate the fraction:

\[
3y - 6x - yx = 0
\]

### Step 5: Solve for \(x\)
Factor out \(x\):

\[
3y = x(y + 6)
\]

Finally, solve for \(x\):

\[
x = \frac{3y}{y + 6}
\]

So, the correct answer is **option B**:

\[
x = \frac{3y}{y + 6}
\]

---

Do you want more details on any step or have any other questions? Here are some related questions:

1. How do you solve similar equations with fractions?
2. Can you explain factoring in more detail?
3. What are the steps to simplify equations with multiple variables?
4. How do you handle equations with multiple terms involving the variable?
5. How does distributing work in equations?

**Tip:** When solving equations with variables in the denominator, multiplying both sides by the denominator is a useful technique to eliminate fractions.

Solve the equation \(\frac{y - 2x}{x} = \frac{y}{3}\) for x.

Learn how to solve the algebraic equation \(\frac{y - 2x}{x} = \frac{y}{3}\) step by step. This problem involves manipulating equations with fractions, distributing terms, and solving for a variable. Suitable for students in Grades 9-11.

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