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Question

Solve the equation:

x-1=1-x


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Solution

Solving the equation using function property :

x-1=1-x

x-1=x-1 for all x1

x-1=-x-1for all x<1

Case 1: When x1

x-1=1-x

x-1=1-x

x+x=1+1

2x=2

x=1

Case 2:When x<1

x-1=1-x

-(x-1)=1-x

-x+1=1-x

1-x=1-x

Here, the solution will be all the real values of x, which are less than 1.
Therefore, the solution for x is (-,1]


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