|x-2|=3

To solve the equation |x-2| = 3, we need to consider two cases: when x-2 is positive and when x-2 is negative.

Case 1: x-2 is positive In this case, the equation becomes x-2 = 3. Solving for x: x - 2 = 3 x = 3 + 2 x = 5

Case 2: x-2 is negative In this case, the equation becomes -(x-2) = 3. Solving for x: -(x-2) = 3 -x + 2 = 3 -x = 1 x = -1

Therefore, the solutions to the equation |x-2| = 3 are x = 5 and x = -1.