To solve the inequality:

$2(x + 4) > -12$

Step 1: Distribute the 2 on the left-hand side.

$2x + 8 > -12$

Step 2: Subtract 8 from both sides.

$2x > -12 - 8$ $2x > -20$

Step 3: Divide both sides by 2 to solve for $x$.

$x > \frac{-20}{2}$ $x > -10$

Final Answer:

$x > -10$

Let me know if you need more details or have any questions!

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Here are five related questions to expand on this:

1. How do you solve inequalities that involve division by a negative number?
2. Can you explain how to represent $x > -10$ on a number line?
3. What happens if the inequality had been $2(x + 4) < -12$ instead?
4. How would the solution change if the inequality had absolute values involved, e.g., $2|x + 4| > -12$?
5. What is the difference between strict inequalities ($>$) and non-strict inequalities ($\geq$)?

Tip: Always reverse the inequality sign when multiplying or dividing both sides by a negative number!