The equation you provided is:

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

### Step 1: Combine like terms (the terms involving \(x\)).
We need to find a common denominator to combine the fractions:

- The least common denominator of 3 and 5 is 15.

So, we rewrite the equation:

\[
x - \frac{5}{15}x - \frac{6}{15}x = y
\]

### Step 2: Combine the fractions.

\[
x - \left(\frac{5}{15}x + \frac{6}{15}x\right) = y
\]
\[
x - \frac{11}{15}x = y
\]

### Step 3: Simplify the expression.
\(x\) can be thought of as \(\frac{15}{15}x\), so:

\[
\frac{15}{15}x - \frac{11}{15}x = y
\]
\[
\frac{4}{15}x = y
\]

### Step 4: Solve for \(x\).
Multiply both sides of the equation by \(\frac{15}{4}\) to isolate \(x\):

\[
x = \frac{15}{4}y
\]

Thus, the solution is:

\[
x = \frac{15}{4}y
\]

Would you like more details on any step? 

Here are some related questions:
1. How do you solve equations with more complex fractions?
2. What happens if you have a fraction with variables in the denominator?
3. How do you factor expressions involving multiple terms of \(x\)?
4. Can this type of equation be graphed, and how?
5. What if I want to solve for \(y\) in terms of \(x\)?

**Tip**: Always check for common denominators when combining terms with fractions to simplify your calculations.

Learn how to solve the linear equation x - 1/3x - 2/5x = y by combining like terms and solving for x. This step-by-step solution covers key algebraic concepts such as working with fractions and isolating variables. Suitable for students in Grades 8-10.

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