What is the value of x if 1/(x) + 1/(2x) = 1/2. x

To solve the equation \(\frac{1}{x} + \frac{1}{2x} = \frac{1}{2}\), let's follow these steps:

1. **Find a common denominator** on the left side:
   \[
   \frac{1}{x} + \frac{1}{2x} = \frac{2 + 1}{2x} = \frac{3}{2x}
   \]
   So the equation becomes:
   \[
   \frac{3}{2x} = \frac{1}{2}
   \]

2. **Cross multiply** to eliminate the fractions:
   \[
   3 \cdot 2 = 1 \cdot 2x
   \]
   \[
   6 = 2x
   \]

3. **Solve for \(x\)** by dividing both sides by 2:
   \[
   x = \frac{6}{2} = 3
   \]

Thus, the value of \(x\) is \( \boxed{3} \).

Would you like more details or have any questions?

Here are five related questions:
1. What happens if the equation was \( \frac{1}{x} + \frac{1}{3x} = \frac{1}{2} \)?
2. How do you solve equations with more complex fractions?
3. Can you explain how to solve the equation if it was \( \frac{1}{x} - \frac{1}{2x} = \frac{1}{2} \)?
4. What are the implications of \(x\) being negative in this equation?
5. How would the solution change if the equation was \( \frac{1}{x} + \frac{1}{2x} = \frac{3}{2} \)?

**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 1/x + 1/2x = 1/2 with a detailed step-by-step solution. This problem involves solving equations with fractions and is suitable for students in Grades 7-9.

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