Answer :

x≠1, as it will lead equation unmeaningful.


Now, on subtracting 2 from both the sides, we get–



Now, 3 case arises:


Case 1:1<x<∞


For this case, |2x–1|=2x–1 and |x–1|=x–1






x ϵ (1, ∞ ) …(1)


Case 2:


For this case: |2x–1|=2x–1 and |x–1|=–(x–1)







…(2)


Case 3:


For this case: |2x–1|=–(2x–1) and |x–1|=–(x–1)






Which is not possible, hence, this will give no solution.


(from 1 and 2)


We can verify the answers using graph as well.



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