Question

Solve for x and simplify the answer fully.

2x-2/8 = x+2/9

Answer 1

We start with the equation:

\[
\frac{2x - 2}{8} = \frac{x + 2}{9}
\]

First, we can eliminate the fractions by cross-multiplying:

\[
9(2x - 2) = 8(x + 2)
\]

Expanding both sides:

\[
18x - 18 = 8x + 16
\]

Next, we’ll move the terms involving \(x\) to one side and the constant terms to the other side. Subtract \(8x\) from both sides:

\[
18x - 8x - 18 = 16
\]

Which simplifies to:

\[
10x - 18 = 16
\]

Now, add 18 to both sides:

\[
10x = 34
\]

Finally, divide by 10:

\[
x = \frac{34}{10}
\]

This can be simplified:

\[
x = \frac{17}{5}
\]

Thus, the solution is:

\[
\boxed{\frac{17}{5}}
\]