The answer is No Solutions! Here's how
1. Subtract 5 from both sides |x-1|=2-5
2. Simplify 2−5 to −3 |x-1|=-3
3. Break down the problem into these 2 equations
x-1=-3 and -(x-1)=-3
4. Solve the 1st equation: x=-2
5. Solve the 2nd equation: x=4
6. Collect all solutions x=-2,4
7. Check first solution: When x=-2x=−2, the original equation |x-1|+5=2∣x−1∣+5=2 does not hold true. We will drop x=-2x=−2 from the solution set.
8. Check second solution: When x=4x=4, the original equation |x-1|+5=2∣x−1∣+5=2 does not hold true. We will drop x=4x=4 from the solution set.
So there are no solutions
All the best!