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I can see that the problem you're solving involves an inequality: \( 6x - 12 < -24 \). Let's work through the steps using the addition and multiplication principles:

### Step-by-step Solution:
1. **Start with the given inequality:**
   \[
   6x - 12 < -24
   \]

2. **Add 12 to both sides** to isolate the term with \( x \):
   \[
   6x - 12 + 12 < -24 + 12
   \]
   Simplifying:
   \[
   6x < -12
   \]

3. **Divide by 6** to solve for \( x \):
   \[
   x < \frac{-12}{6}
   \]
   Simplifying:
   \[
   x < -2
   \]

### Answer:
The solution set is \( \{ x \mid x < -2 \} \).

Now, let's look at the multiple-choice options you provided:

- A: \( \{ x \mid x \geq -2 \} \)
- B: \( \{ x \mid x > -2 \} \)
- C: \( \{ x \mid x \leq -2 \} \)
- D: \( \{ x \mid x < -2 \} \)

The correct answer is **D**.

---

Would you like more details on any step or have any questions?  
Here are five related questions you might want to explore:

1. How do you graph the solution of \( x < -2 \) on a number line?
2. What happens if the inequality had been \( 6x - 12 > -24 \)?
3. How does dividing by a negative number affect inequalities?
4. What are the properties of inequalities when multiplying or dividing?
5. How would the inequality change if the expression involved \( |6x - 12| \)?

**Tip:** Always reverse the inequality sign when you multiply or divide both sides by a negative number!

Solve the inequality 6x - 12 < -24 using addition and multiplication principles and select the correct solution set from the options provided.

Learn how to solve the inequality 6x - 12 < -24 using addition and multiplication principles. This step-by-step guide covers key concepts in solving inequalities, suitable for students in Grades 7-9. Understand how to simplify inequalities and determine the correct solution set.

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