Solve 2/5 + 1/3 = 1/x                                                                                                                             Is there a solution?

We are given the equation:

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

### Step 1: Find a common denominator for the left side of the equation.

The denominators are 5 and 3. The least common denominator (LCD) of 5 and 3 is 15.

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

Now, adding these fractions:

\[
\frac{6}{15} + \frac{5}{15} = \frac{6 + 5}{15} = \frac{11}{15}
\]

### Step 2: Set this equal to the right side of the equation.

\[
\frac{11}{15} = \frac{1}{x}
\]

### Step 3: Solve for \( x \).

To solve for \( x \), we can take the reciprocal of both sides:

\[
x = \frac{15}{11}
\]

### Conclusion:
Yes, there is a solution, and the solution is:

\[
x = \frac{15}{11}
\]

Would you like further details on this solution?

Here are 5 related questions:
1. How do you add fractions with different denominators?
2. What is the least common denominator, and why is it important?
3. Can we use a different method to solve this equation?
4. What happens if \( x \) was negative in this type of equation?
5. How do you verify the solution of a fractional equation?

**Tip:** Always simplify the fractions before adding or subtracting, if possible, to make calculations easier.

Solve 2/5 + 1/3 = 1/x. Is there a solution?

Learn how to solve the equation 2/5 + 1/3 = 1/x with step-by-step instructions. This guide covers key concepts in adding fractions, finding the least common denominator, and applying reciprocal rules. Suitable for students in Grades 6-8.

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