RD Sharma - Mathematics

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.



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