Let's solve the given equation step by step. The equation is:

$\frac{2x + 5}{3x - 4} = \frac{9}{2}$

Step 1: Cross-Multiply

To eliminate the fractions, cross-multiply: $2(2x + 5) = 9(3x - 4)$

Expand both sides: $4x + 10 = 27x - 36$

Step 2: Simplify and Solve for $x$

Move all terms involving $x$ to one side and constants to the other: $4x - 27x = -36 - 10$

Simplify: $-23x = -46$

Divide both sides by $-23$: $x = 2$

Final Answer:

$x = 2$

Would you like a detailed explanation of each step? Let me know if you have questions! 😊

Related Questions:

1. How can cross-multiplication help in solving rational equations?
2. What happens if there’s a zero in the denominator of a fraction?
3. How do you verify solutions for rational equations?
4. Can you solve $\frac{5x + 3}{2x - 1} = \frac{7}{3}$?
5. How does simplifying equations change when dealing with inequalities?

Tip:

Always check your solutions by substituting them back into the original equation to ensure there are no undefined values (e.g., zero denominators).