Question

what is the solution set of the equation Ix-1I=3?

Answer 1

|x-1| Means the absolute value (always positive) of x-1.

So that means that x-1 = 3 or x-1 = -3
(if x-1 = -3, then the absolute value (ignoring the negative sign) would be 3)

Solve both of those equations, you'll get two answers.
The solution set is {answer1, answer2}