To solve the equation:

$\frac{x}{8} = \frac{-2}{11}$

We can cross-multiply to eliminate the denominators:

$x \cdot 11 = -2 \cdot 8$

Simplifying both sides:

$11x = -16$

Now, solve for $x$ by dividing both sides by 11:

$x = \frac{-16}{11}$

So, the solution is:

$x = \frac{-16}{11}$

Would you like further details or clarifications on any part of the solution?

Here are 5 related questions to explore:

1. How would you solve an equation like $\frac{x}{3} = \frac{4}{5}$?
2. What happens when both sides of an equation have negative fractions?
3. How do you handle variables in denominators?
4. Can you solve equations with cross-multiplying when the denominators are variables?
5. How would you solve an equation where both fractions have polynomials in the numerator?

Tip: When solving equations with fractions, cross-multiplying is a quick and effective way to eliminate the denominators.