The inequality is:

$|2x + 6| \geq 12$

Step 1: Understand the absolute value

The inequality $|A| \geq B$ means $A \leq -B$ or $A \geq B$. Applying this to $2x + 6$, we get two cases:

1. $2x + 6 \geq 12$
2. $2x + 6 \leq -12$

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Step 2: Solve each case

Case 1: $2x + 6 \geq 12$

$2x \geq 12 - 6$ $2x \geq 6$ $x \geq 3$

Case 2: $2x + 6 \leq -12$

$2x \leq -12 - 6$ $2x \leq -18$ $x \leq -9$

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Step 3: Combine the solutions

The solution is: $x \geq 3 \quad \text{or} \quad x \leq -9$

In interval notation: $x \in (-\infty, -9] \cup [3, \infty)$

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Would you like me to explain any step in more detail? Here are some related questions to practice:

1. How do you solve $|x - 4| \leq 8$?
2. What is the general method for solving absolute value inequalities?
3. How do you graph solutions to $|x + 5| \geq 10$?
4. Can absolute value inequalities have no solution? Why or why not?
5. How does changing $\geq$ to $>$ affect the solution?

Tip: Always split absolute value inequalities into two cases and handle each separately!