To solve the equation \( \frac{6}{3x} + \frac{1}{x} = 2 \), let's go through the steps systematically:

### Step 1: Simplify the equation
First, simplify the fraction \( \frac{6}{3x} \):
\[
\frac{6}{3x} = \frac{2}{x}
\]
So, the equation becomes:
\[
\frac{2}{x} + \frac{1}{x} = 2
\]

### Step 2: Combine like terms
Combine the fractions on the left-hand side:
\[
\frac{2}{x} + \frac{1}{x} = \frac{2 + 1}{x} = \frac{3}{x}
\]
Now, the equation is:
\[
\frac{3}{x} = 2
\]

### Step 3: Solve for \( x \)
To solve for \( x \), multiply both sides of the equation by \( x \) to get rid of the fraction:
\[
3 = 2x
\]

Now, divide both sides by 2:
\[
x = \frac{3}{2}
\]

### Final Answer:
\[
x = \frac{3}{2} \quad \text{or} \quad x = 1.5
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How would the solution change if the equation was \( \frac{6}{3x} + \frac{1}{x} = 3 \)?
2. What if the equation was \( \frac{6}{3x} - \frac{1}{x} = 2 \)?
3. How would you solve \( \frac{6}{3x} + \frac{1}{x} = 0 \)?
4. What happens if we have \( \frac{6}{3x} + \frac{2}{x} = 2 \)?
5. How do you solve the equation \( \frac{4}{x} + \frac{2}{x} = 3 \)?

**Tip:** When combining like terms with fractions, always make sure the denominators are the same before adding or subtracting.

Discover how to solve the rational equation 6/3x + 1/x = 2 with a clear, step-by-step solution. This example covers key algebraic concepts like simplifying fractions and combining like terms, making it perfect for students in Grades 7-9.

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