2 over 6 plus 1 over 2x equals 1 over 1 over 3

We are given the equation:

\[
\frac{2}{6} + \frac{1}{2x} = \frac{1}{\frac{1}{3}}
\]

### Step 1: Simplify the fractions
First, simplify the fractions on both sides of the equation.

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

Now, the equation becomes:

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

### Step 2: Simplify the right-hand side
The right-hand side of the equation can be simplified:

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

Now the equation is:

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

### Step 3: Isolate \(\frac{1}{2x}\)
Subtract \(\frac{1}{3}\) from both sides:

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

To subtract these, convert 3 into a fraction with a denominator of 3:

\[
3 = \frac{9}{3}
\]

Now subtract:

\[
\frac{1}{2x} = \frac{9}{3} - \frac{1}{3} = \frac{8}{3}
\]

### Step 4: Solve for \(x\)
Now, cross-multiply to solve for \(x\):

\[
1 \cdot 2x = 8 \cdot 3
\]

\[
2x = 24
\]

Divide both sides by 2:

\[
x = \frac{24}{2} = 12
\]

### Final Answer:
\[
x = 12
\]

Would you like further details on any step or have questions?

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Here are 5 related questions to explore:

1. What is the process for solving equations with multiple fractions?
2. How do you handle complex fractions like \(\frac{1}{\frac{1}{a}}\)?
3. What are some tips for simplifying algebraic fractions?
4. How can you verify solutions in equations with variables?
5. How do equations with variables in denominators differ from those without?

**Tip:** Always simplify fractions first to reduce the complexity of the equation!

Learn how to solve the algebraic equation 2/6 + 1/(2x) = 1/(1/3) with step-by-step instructions. This problem covers key concepts such as simplifying fractions and using cross-multiplication, ideal for students in Grades 6-8.

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