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.