Let's solve the equation:

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

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) of the fractions. The denominators are 5, 3, and 2. The LCD of these numbers is 30.

Multiply every term in the equation by 30:

\[
30 \cdot \left(\frac{x}{5}\right) + 30 \cdot \left(\frac{x}{3}\right) - 30 \cdot 1 = 30 \cdot \left(\frac{x}{2}\right)
\]

Simplify:

\[
6x + 10x - 30 = 15x
\]

### Step 2: Simplify the equation
Combine like terms:

\[
6x + 10x - 15x = 30
\]

\[
x = 30
\]

### Solution:
The solution to the equation is \( x = 30 \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you find the least common denominator of multiple fractions?
2. What is the general method for solving linear equations with fractions?
3. How can you verify the solution of a linear equation?
4. What if the equation had been \( \frac{x}{5} + \frac{x}{3} - 1 = \frac{x}{4} \)?
5. How would the solution change if the right side of the equation was \( \frac{x}{2} + 2 \)?
6. Can the same approach be applied to equations with more complex fractions?
7. How do you handle equations with variables in the denominators?
8. What if the equation had a quadratic term, such as \( \frac{x^2}{5} + \frac{x}{3} - 1 = \frac{x}{2} \)?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation involving fractions: x/5 + x/3 - 1 = x/2 with a step-by-step solution. This problem covers solving linear equations with fractions, including the process of eliminating fractions by finding a common denominator. Suitable for students in Grades 7-9.

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