x≠1, as it will lead equation unmeaningful.
Now, on subtracting 2 from both the sides, we get–
Now, 3 case arises:
For this case, |2x–1|=2x–1 and |x–1|=x–1
⇒ x ϵ (1, ∞ ) …(1)
For this case: |2x–1|=2x–1 and |x–1|=–(x–1)
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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