Question

Solve for x and simplify the answer fully.

x-8/x-2=7/8

Answer 1

To solve the equation

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

we will cross-multiply to eliminate the fractions.

Cross-multiplying gives:

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

Expanding both sides:

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

Now, let's isolate \(x\). First, subtract \(7x\) from both sides:

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

which simplifies to:

\[
x - 64 = -14.
\]

Next, add 64 to both sides:

\[
x = 64 - 14,
\]

which simplifies to:

\[
x = 50.
\]

Finally, we can summarize our result:

\[
\boxed{50}.
\]