The equation you provided in the image appears to be:

$\frac{2x - 1}{3} = \frac{2x - 8}{2} + 1$

Let's solve it step by step:

1. First, eliminate the denominators by multiplying through by the least common multiple (LCM) of 3 and 2, which is 6.

$6 \times \left(\frac{2x - 1}{3}\right) = 6 \times \left(\frac{2x - 8}{2}\right) + 6 \times 1$

This simplifies to:

$2(2x - 1) = 3(2x - 8) + 6$

2. Expand both sides:

$4x - 2 = 6x - 24 + 6$

Simplify the constants:

$4x - 2 = 6x - 18$

3. Move all terms involving $x$ to one side and constants to the other:

$4x - 6x = -18 + 2$

$-2x = -16$

4. Solve for $x$:

$x = \frac{-16}{-2} = 8$

Thus, the solution to the equation is $x = 8$.

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. How can you check if the solution $x = 8$ satisfies the original equation?
2. What are the possible methods to solve equations with fractions?
3. How would you handle the equation if a different LCM was used?
4. What happens if we encounter negative signs on both sides during simplification?
5. Can you apply the same method to solve systems of equations involving fractions?

Tip: When solving equations with fractions, it's often useful to clear the denominators early to simplify the process.