https://file.aiquickdraw.com/mathbot/file/1725556280201kjwbkijb.jpg

The equation in the image is:

\[
\frac{x}{6} = -9
\]

### Step-by-Step Solution Using the Multiplication Principle:
To solve for \( x \), use the multiplication principle. This principle allows you to eliminate the fraction by multiplying both sides of the equation by the denominator of the fraction (in this case, 6).

1. Multiply both sides by 6:
   \[
   6 \times \frac{x}{6} = 6 \times (-9)
   \]

2. Simplify both sides:
   \[
   x = -54
   \]

### Check the Solution:
To check, substitute \( x = -54 \) back into the original equation:
\[
\frac{-54}{6} = -9
\]
Since both sides of the equation are equal, the solution is correct.

The final solution is:
\[
x = -54
\]

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Do you need more details on any step or have any further questions?

### Related Questions:
1. How do you solve an equation with fractions on both sides?
2. Can the multiplication principle be used for inequalities?
3. How would the solution change if the equation were \(\frac{x}{-6} = -9\)?
4. What if the equation had decimals instead of fractions, such as \(x/2.5 = -9\)?
5. What does it mean when there's no solution or an infinite number of solutions to a linear equation?

**Tip:** Always perform a check after solving an equation to ensure the solution is correct!

Solve using the multiplication principle: x / 6 = -9.

Learn how to solve the linear equation x / 6 = -9 using the multiplication principle. Follow the step-by-step solution and check the result. Suitable for students in Grades 6-8.

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