Let's solve the equation \( \frac{X}{3} - 2X + \frac{1}{3} = X - \frac{3}{5} \).

### Step 1: Clear the fractions
To eliminate the fractions, we can multiply every term by the least common denominator (LCD) of 3 and 5, which is 15.

\[
15 \times \left(\frac{X}{3}\right) - 15 \times 2X + 15 \times \left(\frac{1}{3}\right) = 15 \times X - 15 \times \left(\frac{3}{5}\right)
\]

This simplifies to:

\[
5X - 30X + 5 = 15X - 9
\]

### Step 2: Combine like terms
Now, combine the \( X \) terms and the constants:

\[
5X - 30X = 15X - 9 - 5
\]

This simplifies to:

\[
-25X = 15X - 14
\]

### Step 3: Move all terms involving \( X \) to one side
Add \( 25X \) to both sides to get:

\[
0 = 40X - 14
\]

### Step 4: Solve for \( X \)
Now, solve for \( X \) by isolating it:

\[
40X = 14
\]

\[
X = \frac{14}{40}
\]

Simplify the fraction:

\[
X = \frac{7}{20}
\]

### Final Answer:
\[
X = \frac{7}{20}
\]

Would you like more details, or do you have any questions about the solution?

Here are 5 related questions for further practice:

1. How would you solve \( \frac{2X}{5} - \frac{3}{2} = \frac{X}{3} + \frac{1}{6} \)?
2. Can you solve \( 4X - \frac{2}{3} = \frac{X}{2} + \frac{5}{4} \)?
3. What is the solution to \( \frac{3X}{4} - 5X + \frac{2}{3} = 2X - \frac{7}{8} \)?
4. How would you approach \( \frac{X}{2} + \frac{3X}{5} = \frac{X}{4} + \frac{1}{2} \)?
5. Solve \( \frac{X+2}{3} - X = \frac{1}{5} \).

**Tip:** Always clear fractions early in the equation by multiplying by the least common denominator; this simplifies the equation and reduces potential errors.

Learn how to solve equations involving fractions step-by-step with a detailed solution. This problem covers key concepts such as eliminating fractions, combining like terms, and isolating variables. Suitable for high school students.

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