Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 11 of Exercise 15.3
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
11
Solve each of the following system of equations in R.
Subtracting 3 from both sides, we get–
|x+1|+|x|–3>0
For this, we have 3 cases,
Case 1:–∞ <x<–1
For this, |x+1|=–(x+1) and |x|=–x
–(x+1)–x–3>0
–2x–1–3>0
2x+4<0
x<–2
⇒ x ϵ (–∞ , –2) …(1)
Case 2: –1<x<0
For this, |x+1|=x+1 and |x|=–x
x+1–x–3>0
–2>0
Which is absurd, thus it leads to no solution.
Case 3: 0<x<∞
For this, |x+1|=x+1 and |x|=x
x+1+x–3>0
2x–2>0
x>1
⇒ x ϵ (1 , ∞ ) …(2)
⇒ xϵ (–∞ , –2)⋃ (1 , ∞ ) (from 1 and 2)
We can verify the answers using graph as well.
