To solve the equation \( 3(x - 2) = 9x \), let's follow these steps:

1. **Expand the left side**: Distribute the 3 across the terms inside the parentheses.
   \[
   3 \cdot x - 3 \cdot 2 = 3x - 6
   \]
   So, the equation becomes:
   \[
   3x - 6 = 9x
   \]

2. **Move all terms involving \(x\) to one side of the equation**: Subtract \(3x\) from both sides.
   \[
   3x - 6 - 3x = 9x - 3x
   \]
   Simplifying, we get:
   \[
   -6 = 6x
   \]

3. **Solve for \(x\)**: Divide both sides by 6.
   \[
   x = \frac{-6}{6} = -1
   \]

So, the solution is \( x = -1 \).

Would you like further details or have any questions?

Here are five related questions you might find helpful:
1. What happens if the equation has no solution?
2. How do you solve equations with variables on both sides and parentheses?
3. What is the process for solving an equation with fractions?
4. How can you check if the solution to an equation is correct?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always simplify the equation step by step to avoid errors and ensure accuracy.

Learn how to solve the linear equation 3(x - 2) = 9x with a step-by-step solution. This problem covers essential algebraic concepts, including distribution and properties of equality. Suitable for students in Grades 6-8.

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