https://file.aiquickdraw.com/mathbot/file/1725976046263nxr6owej.jpg

The equation in the image is:

\[
\frac{3}{x} = \frac{4}{3x} - \frac{10}{3}
\]

Let's solve it step by step.

### Step 1: Eliminate the fractions by multiplying through by a common denominator.
The common denominator of \(x\), \(3x\), and 3 is \(3x\). Multiply the entire equation by \(3x\):

\[
3x \cdot \frac{3}{x} = 3x \cdot \frac{4}{3x} - 3x \cdot \frac{10}{3}
\]

This simplifies as follows:

\[
3(3) = 4 - 10x
\]

\[
9 = 4 - 10x
\]

### Step 2: Solve for \(x\).

First, move the 4 to the other side by subtracting it from both sides:

\[
9 - 4 = -10x
\]

\[
5 = -10x
\]

Now, divide by \(-10\):

\[
x = \frac{5}{-10} = -\frac{1}{2}
\]

### Final Answer:
\[
x = -\frac{1}{2}
\]

Let me know if you'd like more details or explanations.

---

Here are 5 related questions to further expand your understanding:
1. How do you find the least common denominator when solving equations with fractions?
2. What happens if you multiply both sides of an equation by a negative number?
3. How can you verify that the solution to a fractional equation is correct?
4. What is the importance of clearing fractions before solving?
5. How does solving rational equations differ from solving regular linear equations?

**Tip**: When solving equations with fractions, it's often easier to clear the fractions early on by multiplying through by the least common denominator.

Learn how to solve the equation 3/x = 4/3x - 10/3 step-by-step. This problem focuses on algebraic manipulation and clearing fractions using the least common denominator. Ideal for students in Grades 8-10.

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