∣x−2∣<12

To solve this inequality, we must consider two cases:

Case 1: x - 2 is positive:
If x - 2 is positive, then |x - 2| is equal to x - 2. Therefore, the inequality can be rewritten as:
x - 2 < 12

Adding 2 to both sides:
x < 14

Case 2: x - 2 is negative:
If x - 2 is negative, then |x - 2| is equal to -(x - 2) or 2 - x. Therefore, the inequality can be rewritten as:
2 - x < 12

Adding x to both sides:
2 < x + 12

Subtracting 12 from both sides:
-10 < x

Combining the two cases, we find that the solution to the inequality is:
-10 < x < 14