Question 97643
Since the absolute value of x-1 is given to be 1-x, we will presume that there can be two values for x-1-----a negative or a positive.


If x-1 is negative,

x-1=-(1-x)
x-1=x-1

This is true for all real numbers.


If x-1 is positive, 

x-1=1-x
x-1+x=1-x+x
2x-1=1
2x-1+1=1+1
2x=2
x=1

Thus if x-1 is negative, x=1.




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