**Solve the following equation for x:**   
**9/(4x) + 1/3 = 5/(2x)**

We are tasked with solving the equation:

\[
\frac{9}{4x} + \frac{1}{3} = \frac{5}{2x}
\]

### Step-by-Step Solution:

1. **Get rid of the fractions** by finding the least common denominator (LCD). The denominators in the equation are \(4x\), \(3\), and \(2x\). The least common denominator of these terms is \(12x\).

2. **Multiply the entire equation by the LCD** \(12x\) to eliminate the fractions:

\[
12x \times \left( \frac{9}{4x} \right) + 12x \times \left( \frac{1}{3} \right) = 12x \times \left( \frac{5}{2x} \right)
\]

3. Simplifying each term:

- \( 12x \times \frac{9}{4x} = 3 \times 9 = 27 \)
- \( 12x \times \frac{1}{3} = 4x \)
- \( 12x \times \frac{5}{2x} = 6 \times 5 = 30 \)

The equation now becomes:

\[
27 + 4x = 30
\]

4. **Solve for \(x\)**:

Subtract 27 from both sides:

\[
4x = 30 - 27
\]
\[
4x = 3
\]

Now, divide both sides by 4:

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

### Final Answer:

The solution is \( x = \frac{3}{4} \).

---

Would you like any further clarification or details? Here are some related questions:

1. How do you solve an equation with multiple fractions in it?
2. What is the least common denominator (LCD) in other types of equations?
3. Can you simplify equations by factoring after eliminating fractions?
4. How would this solution change if we had different constants in the equation?
5. What are some common methods for handling algebraic fractions?

**Tip:** Always try to eliminate fractions first by multiplying through by the least common denominator (LCD), as it simplifies the equation and makes solving easier.

Solve the following equation for x: 9/(4x) + 1/3 = 5/(2x)

Learn how to solve the algebraic equation 9/(4x) + 1/3 = 5/(2x) with a detailed step-by-step solution. This problem covers key algebraic concepts like solving equations with fractions and using the least common denominator. Suitable for students in Grades 8-10.

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