The equation given in the image is:

$\frac{2(x - 3)}{3} - \frac{x - 2}{4} = 1$

Steps to Solve for $x$:

1. Eliminate Fractions by Finding the Least Common Denominator (LCD):

   • The denominators are $3$ and $4$, so the LCD is $12$.
   • Multiply through by $12$ to eliminate the denominators: $12 \cdot \frac{2(x - 3)}{3} - 12 \cdot \frac{x - 2}{4} = 12 \cdot 1$
   • Simplify each term: $4 \cdot 2(x - 3) - 3 \cdot (x - 2) = 12$

2. Distribute the Terms:

   • Expand: $8(x - 3) - 3(x - 2) = 12$
   • Simplify further: $8x - 24 - 3x + 6 = 12$

3. Combine Like Terms:

   • Combine $x$-terms and constants: $(8x - 3x) + (-24 + 6) = 12$ $5x - 18 = 12$

4. Isolate $x$:

   • Add $18$ to both sides: $5x = 30$
   • Divide by $5$: $x = 6$

Final Answer:

$x = 6$

Let me know if you would like a deeper explanation or additional steps!

5 Related Questions:

1. What is the importance of finding the LCD when solving equations with fractions?
2. How can you verify the solution to an equation with fractions?
3. What happens if you forget to distribute terms correctly when solving?
4. How do you solve equations involving more complex fractions?
5. Can this method be applied to inequalities? If so, how?

Tip: Always double-check your work by substituting your solution back into the original equation!