Let's solve the equation step by step:

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

### Step 1: Eliminate the denominators by multiplying through by \( 3x \), which is the least common denominator (LCD).

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

Simplifying each term:

\[
3x \times \frac{3}{x} = 9
\]
\[
3x \times \frac{4}{3x} = 4
\]
\[
3x \times \frac{10}{3} = 10x
\]

So the equation becomes:

\[
9 = 4 - 10x
\]

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

First, move the constant terms to one side:

\[
9 - 4 = -10x
\]

This simplifies to:

\[
5 = -10x
\]

Now, solve for \( x \):

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

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

Would you like more details on any part of this solution, or do you have any further questions?

### Related Questions:
1. How do you find the least common denominator in an equation?
2. What are some techniques to solve rational equations?
3. How can we verify if \( x = -\frac{1}{2} \) is correct?
4. What happens if there’s a restriction on \( x \) in a rational equation?
5. Can you explain how to handle equations with multiple terms involving variables in denominators?

### Tip:
Always check for extraneous solutions when solving equations that involve variables in the denominator!

Discover how to solve the rational equation 3/x = 4/3x - 10/3 with a clear step-by-step explanation. Learn key algebraic concepts, including the use of the least common denominator (LCD) and linear equation solving techniques. This solution is suitable for students in Grades 9-11.

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