How do you solve |x-1| + 5=2?

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!