∣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