Answer: No solutions
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Step-by-step explanation:
Start things off by subtracting 5 from both sides
|x-1|+5 = 2
|x-1|+5-5 = 2-5
|x-1| = -3
We cannot go any further after this point. The result of any absolute value is never negative. The absolute value represents distance from some number to 0. For example, saying |-7| = 7 means -7 is seven units away from 0 on a number line. Negative distance does not make sense.
So going back to |x-1| = -3 makes no sense as well. There are no numbers we can plug in for x to have |x-1| = -3 be true.
The equation |x-1| = -3 has no solutions, so the original equation doesn't have any solutions either.