Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 7 of Exercise 15.3
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7
Solve each of the following system of equations in R.
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.
