RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 15. Linear Inequations

Subject: Maths - Class 11th

Q. No. 24 of Exercise 15.1

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24

Solve the following linear inequations in R

Given









For this inequation to be true, there are two possible cases.


i. x – 3 > 0 and x + 6 < 0


x – 3 + 3 > 0 + 3 and x + 6 – 6 < 0 – 6


x > 3 and x < –6


x (3, ∞) (–∞, –6)


However, (3, ∞) (–∞, –6) =


Hence, this case is not possible.


ii. x – 3 < 0 and x + 6 > 0


x – 3 + 3 < 0 + 3 and x + 6 – 6 > 0 – 6


x < 3 and x > –6


x (–∞, 3) (–6, ∞)


However, (–∞, 3) (–6, ∞) = (–6, 3)


Hence, x (–6, 3)


Thus, the solution of the given inequation is (–6, 3).


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