Parallel DC Circuits Practice Worksheet With Answers Worksheet ... - Free Printable

To solve the problem, let's carefully analyze the given information and proceed step by step.

Problem Statement:

We are tasked with finding the value of \( x \) in the equation:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{3}{4}
\]

Step-by-Step Solution:

1. Combine the fractions on the left-hand side:
The denominators of the fractions on the left-hand side are \( x \) and \( 2x \). To combine them, we need a common denominator. The least common denominator (LCD) of \( x \) and \( 2x \) is \( 2x \).

Rewrite each fraction with the common denominator \( 2x \):
\[
\frac{1}{x} = \frac{2}{2x} \quad \text{and} \quad \frac{1}{2x} = \frac{1}{2x}
\]

Now, add the fractions:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{2}{2x} + \frac{1}{2x} = \frac{2 + 1}{2x} = \frac{3}{2x}
\]

2. Set up the equation:
Substitute the combined fraction back into the original equation:
\[
\frac{3}{2x} = \frac{3}{4}
\]

3. Eliminate the fractions by cross-multiplying:
Cross-multiply to solve for \( x \):
\[
3 \cdot 4 = 3 \cdot 2x
\]
Simplify both sides:
\[
12 = 6x
\]

4. Solve for \( x \):
Divide both sides of the equation by 6:
\[
x = \frac{12}{6} = 2
\]

Final Answer:

\[
\boxed{2}
\]

Verification:

To ensure the solution is correct, substitute \( x = 2 \) back into the original equation:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{1}{2} + \frac{1}{2 \cdot 2} = \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}
\]
The left-hand side equals the right-hand side, confirming that \( x = 2 \) is indeed the correct solution.

Thus, the final answer is:
\[
\boxed{2}
\]