Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.
If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.
If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.
Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).