Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 10 of Exercise 15.3
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10
Solve each of the following system of equations in R.
We know that, if we take reciprocal of any inequality we need to change the inequality as well.
Also,
|x|–3≠0
⇒ |x|>3 or |x|<3
For |x|<3
⇒ –3<x<3
⇒ x ϵ (–3, 3) …(1)
∴, The equation can be re–written as–
Adding 2 both the sides, we get–
|x|–3+3≥ 2+3
⇒ |x|≥5
We know that,
|x |≥a ⟺ x≤–a or x≥a
Here, a=5
⇒ x≤–5 or x≥5
⇒ x ϵ(–∞,–5 ] or x ϵ[5, ∞) …(2)
⇒ x ϵ(–∞,–5 ] ⋃ (–3, 3) ⋃ [5, ∞) (from 1 and 2)
We can verify the answers using graph as well.
