Let's solve the equation:

\[
\left(x + \frac{1}{3}\right) = \left(x + \frac{2}{5}\right)
\]

First, subtract \(x\) from both sides:

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

Next, check if this statement is true. To compare the fractions, let's find a common denominator.

The least common denominator between 3 and 5 is 15.

Convert the fractions:

\[
\frac{1}{3} = \frac{5}{15}
\]
\[
\frac{2}{5} = \frac{6}{15}
\]

So, we have:

\[
\frac{5}{15} \neq \frac{6}{15}
\]

This equation has no solution because \(\frac{1}{3}\) is not equal to \(\frac{2}{5}\).

### Summary:
There is no value of \(x\) that satisfies the equation \(\left(x + \frac{1}{3}\right) = \left(x + \frac{2}{5}\right)\).

Would you like further details or have any questions?

### Related Questions:
1. What is the general method to solve linear equations?
2. How do you find a common denominator for fractions?
3. What are the properties of equality used in algebra?
4. Can we graphically represent this equation to find the solution?
5. How do we solve equations involving variables on both sides?

### Tip:
Always check the equality of fractions by finding a common denominator or converting them to decimal form.

Learn how to solve the equation (x + 1/3) = (x + 2/5) with a detailed step-by-step solution. This problem involves comparing fractions and using properties of equality to determine why the equation has no solution. Suitable for students in Grades 7-9.

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