The equation you've provided is:

\[
\frac{4}{2x} + 3 = \frac{5}{x} + 4
\]

To solve for \( x \), let's follow these steps:

1. **Simplify the equation**: 

   \[
   \frac{2}{x} + 3 = \frac{5}{x} + 4
   \]

2. **Subtract** \(\frac{2}{x}\) from both sides:

   \[
   3 = \frac{3}{x} + 4
   \]

3. **Subtract 4 from both sides**:

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

4. **Solve for \( x \)** by multiplying both sides by \( x \) and then dividing by -1:

   \[
   x = -3
   \]

So, the solution is \( x = -3 \).

Would you like a more detailed explanation, or do you have any other questions?

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**Tip:** Always check your final answer by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 4/(2x+3) = 5/(x+4) with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations and fractions. Suitable for students in Grades 7-9.

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