To solve the equation:

\[
\frac{1}{3}x = 3x - \frac{2}{5}
\]

let’s isolate \( x \) by following these steps:

1. **Clear the fractions** by finding a common denominator. The denominators here are \( 3 \) and \( 5 \), so we multiply each term by \( 15 \) (the least common multiple of 3 and 5):

   \[
   15 \cdot \frac{1}{3}x = 15 \cdot 3x - 15 \cdot \frac{2}{5}
   \]

2. Simplify each term:

   - \( 15 \cdot \frac{1}{3}x = 5x \)
   - \( 15 \cdot 3x = 45x \)
   - \( 15 \cdot \frac{2}{5} = 6 \)

   This gives us the equation:

   \[
   5x = 45x - 6
   \]

3. **Move all terms involving \( x \) to one side** of the equation. Subtract \( 5x \) from both sides:

   \[
   0 = 40x - 6
   \]

4. **Isolate \( x \)** by adding \( 6 \) to both sides:

   \[
   6 = 40x
   \]

5. **Solve for \( x \)** by dividing both sides by \( 40 \):

   \[
   x = \frac{6}{40} = \frac{3}{20}
   \]

So, the solution is:

\[
x = \frac{3}{20}
\]

Would you like further clarification on any step? 

### Related Questions
1. How do you solve equations with variables on both sides?
2. How do you solve equations with multiple fractions?
3. What are common techniques for clearing fractions in an equation?
4. How can you check if your solution is correct in an equation?
5. What strategies are there for equations that seem complex?

#### Tip
When you have fractions in an equation, clearing the fractions first can make it easier to work with.

Explore a step-by-step solution to solve the linear equation with fractions: 1/3x = 3x - 2/5. This tutorial covers algebraic methods, including clearing fractions and isolating variables. Ideal for students in Grades 8-10 looking to strengthen their algebra skills.

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