To solve the inequality \(-3(w - 1) > 27\), follow these steps:

1. **Distribute the \(-3\)** to both terms inside the parentheses:
   \[
   -3w + 3 > 27
   \]

2. **Subtract 3** from both sides to isolate the term with \(w\):
   \[
   -3w > 24
   \]

3. **Divide both sides by \(-3\)** to solve for \(w\). Remember that dividing or multiplying by a negative number reverses the inequality sign:
   \[
   w < -8
   \]

So, the solution is \(w < -8\).

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would you solve the inequality if it was \(-3(w + 1) > 27\)?
2. What happens to the inequality sign when multiplying or dividing both sides by a negative number?
3. Can you solve the inequality \(-2(2w - 5) \geq 18\)?
4. What is the difference between solving an equation and solving an inequality?
5. How would you graph the solution \(w < -8\) on a number line?

**Tip:** Always remember to flip the inequality sign when you multiply or divide by a negative number.

Learn how to solve the inequality -3(w - 1) > 27 step-by-step with detailed explanations. This problem involves distributing and manipulating inequalities, focusing on algebraic techniques for inequalities. Suitable for students in Grades 7-9.

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