To solve the inequality algebraically:

$|x - 2| < 12$

Step 1: Understand the property of absolute value inequality

For $|a| < b$, this implies: $-b < a < b$

Step 2: Apply this property to the given inequality

Here, $a = x - 2$ and $b = 12$. Therefore: $-12 < x - 2 < 12$

Step 3: Solve for $x$

Add $2$ to all parts of the inequality: $-12 + 2 < x - 2 + 2 < 12 + 2$ $-10 < x < 14$

Final Answer:

The solution to the inequality is: $x \in (-10, 14)$

Would you like further explanations or a graphical representation of this solution?

Related Questions:

1. What happens if the inequality is $|x - 2| \leq 12$?
2. How do we solve $|x - 2| > 12$?
3. What is the graphical interpretation of this inequality on a number line?
4. Can we extend this process to inequalities involving $|ax + b| < c$?
5. How does this solution change if the inequality involves a $\leq$ or $\geq$?

Tip: Always check the steps algebraically by splitting the absolute value into its positive and negative cases to verify correctness.