The equation to solve is:

$\frac{4x - 5}{3x - 5} = \frac{3}{2}$

Steps to solve:

1. Cross-multiply to eliminate the fractions: $2(4x - 5) = 3(3x - 5)$

2. Expand both sides: $8x - 10 = 9x - 15$

3. Simplify the equation: Subtract $8x$ from both sides: $-10 = x - 15$ Add $15$ to both sides: $5 = x$

Solution:

$x = 5$

Would you like a more detailed explanation or clarification?

Here are 5 related questions to explore further:

1. What happens if $3x - 5 = 0$ or if any denominator equals zero?
2. How would this problem change if the right-hand side fraction were $\frac{3}{4}$ instead?
3. How do you check if your solution satisfies the original equation?
4. What strategies can you use to solve similar rational equations?
5. Can this type of equation have more than one solution?

Tip: Always check for restrictions in the domain of rational equations by ensuring the denominators are not zero!