We are given the equation:

\[
\frac{7}{x} = \frac{6}{3x} - 7
\]

### Step 1: Simplify the equation.
First, simplify the fraction on the right-hand side:

\[
\frac{6}{3x} = \frac{2}{x}
\]

So, the equation becomes:

\[
\frac{7}{x} = \frac{2}{x} - 7
\]

### Step 2: Eliminate the fractions.
To eliminate the fractions, multiply the entire equation by \(x\) (assuming \(x \neq 0\)):

\[
7 = 2 - 7x
\]

### Step 3: Solve for \(x\).
Now, solve for \(x\). Subtract 2 from both sides:

\[
7 - 2 = -7x
\]
\[
5 = -7x
\]

Now, divide both sides by \(-7\):

\[
x = \frac{5}{-7} = -\frac{5}{7}
\]

### Final Solution:
\[
x = -\frac{5}{7}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:
1. Solve \(\frac{5}{x} = \frac{10}{4x} - 3\).
2. Solve \( \frac{8}{x} = \frac{4}{5x} - 6 \).
3. Solve \(\frac{9}{x} = \frac{6}{2x} + 4\).
4. Solve \( \frac{12}{x} = \frac{9}{6x} - 5 \).
5. Solve \( 5/x = 1/x + 4 \).

**Tip:** When solving equations with fractions, it's often helpful to eliminate the fractions by multiplying both sides of the equation by the least common denominator (LCD).

Explore how to solve the fractional equation 7/x = 6/3x - 7 with a detailed, step-by-step solution. This problem involves algebraic concepts like simplifying fractions, eliminating fractions by multiplying both sides, and solving linear equations. Suitable for students in Grades 8-10.

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