Bot GPT 4-o mini 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:
\[ \boxed{\frac{17}{5}} \]
1 answer