the question is $$ \frac{x-1}{2}-\frac{5x-3}{3}=3 $$

Thank you for the clarification. The equation provided is:

\[
\frac{x-1}{2} - \frac{5x-3}{3} = 3
\]

### Steps to Solve the Equation

1. **Find the Least Common Denominator (LCD)**: 
   - The denominators are 2 and 3, so the LCD is 6.

2. **Multiply every term by the LCD (6)** to eliminate the fractions:
   \[
   6 \cdot \left(\frac{x-1}{2}\right) - 6 \cdot \left(\frac{5x-3}{3}\right) = 6 \cdot 3
   \]

3. Simplify the equation:
   \[
   3(x - 1) - 2(5x - 3) = 18
   \]

4. Distribute:
   \[
   3x - 3 - 10x + 6 = 18
   \]

5. Combine like terms:
   \[
   -7x + 3 = 18
   \]

6. Subtract 3 from both sides:
   \[
   -7x = 15
   \]

7. Finally, solve for $ x $:
   \[
   x = -\frac{15}{7}
   \]

### Final Answer

\[
x = -\frac{15}{7}
\]

Would you like any further details or have any questions?

### Additional Related Questions:
1. What does it mean when the solution to an equation is a negative fraction?
2. How can we verify that $ x = -\frac{15}{7} $ is the correct solution?
3. What are some common pitfalls when working with equations involving fractions?
4. Can equations with fractions always be solved by eliminating the denominators first?
5. How can this equation be represented graphically?

**Tip:** When working with equations involving fractions, multiplying through by the least common denominator is a powerful strategy to simplify the problem.

Learn how to solve the equation (x-1)/2 - (5x-3)/3 = 3 with detailed step-by-step solutions. Understand the concept of equations involving fractions and apply the distributive property effectively. Suitable for high school students and those preparing for mathematical problem-solving exams.

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