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We are given the equation:

\[
\frac{x - 8}{x - 2} = \frac{7}{8}
\]

To solve for \( x \), let's follow these steps:

### Step 1: Cross-multiply
We can cross-multiply to eliminate the fractions:

\[
8(x - 8) = 7(x - 2)
\]

### Step 2: Expand both sides
Distribute the constants on both sides:

\[
8x - 64 = 7x - 14
\]

### Step 3: Move all \( x \)-terms to one side
Subtract \( 7x \) from both sides to get:

\[
8x - 7x - 64 = -14
\]

This simplifies to:

\[
x - 64 = -14
\]

### Step 4: Solve for \( x \)
Add 64 to both sides:

\[
x = 64 - 14
\]

\[
x = 50
\]

Thus, the solution is \( x = 50 \).

### Final Answer:
\[
x = 50
\]

Would you like a detailed explanation of any specific step, or have any further questions?

Here are 5 related questions you might find useful:
1. How can we check if the solution \( x = 50 \) is correct?
2. What happens if there is no solution to a similar type of equation?
3. How can you manipulate an equation involving fractions differently?
4. What are other methods to solve rational equations?
5. How can you simplify the process of cross-multiplying?

**Tip:** When solving rational equations, always check for extraneous solutions by plugging the solution back into the original equation!

Solve for x and simplify the answer fully: (x - 8) / (x - 2) = 7 / 8

Learn how to solve the rational equation (x - 8) / (x - 2) = 7 / 8 with a detailed step-by-step solution. This problem covers key algebraic concepts, including cross multiplication and solving rational equations. Suitable for students in Grades 8-10.

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