https://file.aiquickdraw.com/mathbot/file/1727438119052iclmwkk1.jpg

The equation presented in the image is:

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

Let's solve this step by step:

### Step 1: Eliminate the fractions
To remove the fractions, multiply every term in the equation by the least common denominator (LCD), which is \( 2x \).

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

### Step 2: Simplify
- \( 2x \times \frac{5}{2x} = 5 \)
- \( 2x \times 3 = 6x \)
- \( 2x \times \frac{4}{x} = 8 \)

This simplifies the equation to:

\[
5 + 6x = 8
\]

### Step 3: Solve for \( x \)
Now, isolate \( x \):
\[
6x = 8 - 5
\]
\[
6x = 3
\]
\[
x = \frac{3}{6} = \frac{1}{2}
\]

### Solution
The value of \( x \) is \( \frac{1}{2} \).

---

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

1. How do you solve equations with multiple fractions?
2. What happens if the denominator includes variables?
3. How do you handle equations with variables on both sides?
4. How can you check if your solution is correct?
5. What methods are available for solving rational equations?

**Tip**: Always check for possible restrictions in rational equations, such as values that make the denominator zero.

Solve the equation: \frac{5}{2x} + 3 = \frac{4}{x}

This page provides a detailed step-by-step guide to solving the rational equation \frac{5}{2x} + 3 = \frac{4}{x}, covering key algebraic concepts such as eliminating fractions by multiplying by the least common denominator. Suitable for students in Grades 8-10.

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