RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 15. Linear Inequations

Subject: Maths - Class 11th

Q. No. 5 of Exercise 15.3

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5

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


xϵ (–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 ….(2)


x ϵ(–∞,–5 ) or x ϵ(5, ∞)


x ϵ(–∞,–5 ) (–3, 3) (5, ∞) (from 1 and 2)


We can verify the answers using graph as well.



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