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The equation you provided is:

\[
\frac{x}{6} = \frac{x + 6}{18}
\]

Let's solve for \(x\).

### Step 1: Eliminate the denominators
Multiply both sides of the equation by 18 to eliminate the denominators.

\[
18 \times \frac{x}{6} = 18 \times \frac{x+6}{18}
\]

Simplifying both sides:

\[
3x = x + 6
\]

### Step 2: Move terms involving \(x\) to one side
Subtract \(x\) from both sides:

\[
3x - x = 6
\]

This simplifies to:

\[
2x = 6
\]

### Step 3: Solve for \(x\)
Divide both sides by 2:

\[
x = 3
\]

Thus, the solution is \(x = 3\).

Would you like a detailed explanation, or do you have any further questions?

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Here are some related questions to consider:

1. What would happen if we changed the equation to \(\frac{x}{4} = \frac{x+8}{12}\)?
2. How would the solution change if the denominators were negative?
3. Can this method be applied to more complex rational equations?
4. What if we started with a quadratic equation instead of a linear one?
5. How can this equation be represented graphically?

**Tip:** When solving equations with fractions, eliminating the denominators early on can simplify the process.

Solve for x: \( \frac{x}{6} = \frac{x+6}{18} \)

Learn how to solve the linear equation \( \frac{x}{6} = \frac{x+6}{18} \) with a detailed step-by-step solution. This problem covers key algebra concepts such as rational equations and basic algebraic manipulation. Suitable for students in Grades 6-8.

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