Let's solve the equation \( \frac{6}{x} = \frac{5}{x} - 7 \).

### Step 1: Eliminate the fractions
Multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)) to eliminate the fractions:

\[
6 = 5 - 7x
\]

### Step 2: Rearrange the equation
Now, let's move the constants to one side and the terms involving \( x \) to the other side:

\[
6 - 5 = -7x
\]

Simplifying this:

\[
1 = -7x
\]

### Step 3: Solve for \( x \)
Now, divide both sides by \( -7 \):

\[
x = \frac{1}{-7} = -\frac{1}{7}
\]

Thus, the solution is:
\[
x = -\frac{1}{7}
\]

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What happens if \( x = 0 \) in the original equation?
2. How would the solution change if the equation was \( \frac{6}{x} = \frac{5}{x} + 7 \)?
3. What are some methods to check if your solution is correct?
4. How can you solve similar equations with more complex fractions?
5. What happens if both sides of the equation involve polynomials?

**Tip:** Always check if the denominator is zero when solving fractional equations, as dividing by zero is undefined.

Learn how to solve the rational equation 6/x = 5/x - 7 with a detailed, step-by-step breakdown. This guide explores core algebraic concepts, including rational equations and solving linear expressions. Ideal for students in Grades 8-10.

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