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The inequality to solve is:

\[
\frac{-12}{11}w > -8
\]

To solve for \( w \), we can follow these steps:

1. **Multiply both sides of the inequality by the reciprocal of \(\frac{-12}{11}\)**, which is \(\frac{-11}{12}\). Since we are multiplying by a negative number, the inequality sign will reverse.

\[
w < \frac{-8 \times (-11)}{12}
\]

2. Simplifying the right side:

\[
w < \frac{88}{12}
\]

3. Further simplify \(\frac{88}{12}\):

\[
w < \frac{22}{3}
\]

Thus, the solution to the inequality is:

\[
w < \frac{22}{3}
\]

Would you like a further explanation or details on the steps? Here are some related questions:

1. How do you handle inequalities when multiplying or dividing by a negative number?
2. What are some techniques to simplify fractions effectively?
3. Can inequalities have multiple solutions?
4. How do inequalities differ from equalities in terms of graphing solutions?
5. How can you check your solution to an inequality?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Resolver la desigualdad para w: (-12/11)w > -8. Simplificar su respuesta tanto como sea posible.

Learn how to solve the inequality (-12/11)w > -8. The step-by-step solution covers multiplying both sides by the reciprocal of (-12/11) and simplifying the result. This problem is ideal for students in Grades 8-10, focusing on algebraic inequalities and properties of inequalities when dealing with negative numbers.

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