To solve the equation \( 92x = \frac{1}{3} \times 27x \) for \(x\), follow these steps:

1. **Write down the equation:**

\[
92x = \frac{1}{3} \times 27x
\]

2. **Simplify the right side of the equation:**

\[
\frac{1}{3} \times 27x = 9x
\]

So the equation becomes:

\[
92x = 9x
\]

3. **Isolate the variable \(x\) by subtracting \(9x\) from both sides:**

\[
92x - 9x = 0
\]

\[
83x = 0
\]

4. **Solve for \(x\):**

\[
x = \frac{0}{83} = 0
\]

So, the value of \(x\) is \(0\).

Would you like more details or have any questions? Here are some related questions you might find useful:

1. What would happen if the right side of the equation had a different coefficient?
2. How do you verify that \(x = 0\) is the correct solution?
3. What is the general process for solving equations where the variable appears on both sides?
4. How does the equation change if instead of \( \frac{1}{3} \times 27x \), you had \( \frac{1}{4} \times 28x \)?
5. What strategies can be used to simplify more complex equations like this one?

**Tip:** When solving equations where the variable appears on both sides, it's crucial to move all terms involving the variable to one side to simplify the equation.

Learn how to solve the equation 92x = (1/3) * 27x to find the value of x. This problem involves basic algebraic operations including multiplication and division. Suitable for students in Grades 6-8.

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