Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 9 of Exercise 15.3
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9
Solve each of the following system of equations in R.
Clearly, |x–2|–2≠0
⇒ |x–2|≠2
⇒ x≠0 and x≠4
Now, 2 case arise:
Case 1:–∞ <x<2
For this, |x–2|=–(x–2)
⇒ x ϵ (0,1] …(1)
Case 2: 2<x<∞
For this, |x–2|=x–2
⇒ x ϵ [3,4) …(2)
⇒ x ϵ (0,1] ⋃ [3, 4) (from 1 and 2)
We can verify the answers using graph as well.
