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The problem asks us to solve the equation \(\frac{x}{6} = -6\) using the multiplication principle, followed by a check of the solution.

### Step-by-Step Solution:

1. **Isolate the variable \(x\):**
   - The equation is \(\frac{x}{6} = -6\).
   - To eliminate the fraction, multiply both sides of the equation by 6:
     \[
     6 \times \frac{x}{6} = 6 \times (-6)
     \]
   - This simplifies to:
     \[
     x = -36
     \]

2. **Check the solution:**
   - Substitute \(x = -36\) back into the original equation:
     \[
     \frac{-36}{6} = -6
     \]
   - The left-hand side simplifies to \(-6\), which matches the right-hand side. Hence, the solution is correct.

### Final Answer:
\[
x = -36
\]

Let me know if you would like further clarification or more details. Here are five related questions to consider:

1. What if the equation was \(\frac{x}{6} = 6\)?
2. How would you solve \(\frac{x}{7} = -5\) using the same method?
3. Can you solve for \(x\) in the equation \(\frac{x}{-4} = 9\)?
4. What is the multiplication principle in general for solving equations?
5. How can you check your answer if the equation involves fractions?

**Tip:** When solving equations with fractions, multiplying by the denominator clears the fraction easily!

Solve using the multiplication principle: x/6 = -6. Perform a check.

Learn how to solve the linear equation x/6 = -6 by applying the multiplication principle. This step-by-step solution involves isolating the variable and checking the answer. Suitable for students in Grades 7-9.

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