Answer: no solution
Explanation: 4|x-1| = -2 (subtract 2 from both sides)
|x-1| =-2/4 (divide by 4 on both sides)
|x-1| =-1/2 (simplify)
|x-1| =-1/2
Anything that comes out of an absolute value sign must be positive. But because this is not, this is no solution.
