To solve the inequality \(-x - 12 > 8\), follow these steps:

1. **Isolate the variable term**:
   \[
   -x - 12 > 8
   \]
   Add 12 to both sides:
   \[
   -x > 20
   \]

2. **Solve for \(x\)**:
   To get \(x\) by itself, multiply both sides of the inequality by \(-1\). Remember, multiplying or dividing an inequality by a negative number reverses the inequality sign:
   \[
   x < -20
   \]

The solution is \(x < -20\).

Would you like a more detailed explanation or have any other questions?

Here are 8 related questions to explore:
1. How do you solve inequalities involving multiplication or division by negative numbers?
2. What are the differences between solving equations and inequalities?
3. How would the solution change if the inequality were \(-x - 12 \geq 8\)?
4. Can you solve the inequality \(2x + 5 > 15\)?
5. What happens if both sides of the inequality involve negative numbers?
6. How do you graph the solution \(x < -20\) on a number line?
7. How do inequalities change when dealing with absolute values?
8. What is the interval notation for the solution \(x < -20\)?

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

Learn how to solve the inequality -x - 12 > 8 with a detailed step-by-step solution. This problem involves isolating variables and multiplying inequalities by negative numbers. Suitable for students in Grades 7-9.

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