Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 28 of Exercise 15.1
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28
Solve the following linear inequations in R
Given 
For this inequation to be true, there are two possible cases.
i. x + 5 > 0 and x – 5 > 0
⇒ x + 5 – 5 > 0 – 5 and x – 5 + 5 > 0 + 5
⇒ x > –5 and x > 5
∴ x ∈ (–5, ∞) ∩ (5, ∞)
However, (–5, ∞) ∩ (5, ∞) = (5, ∞)
Hence, x ∈ (5, ∞)
ii. x + 5 < 0 and x – 5 < 0
⇒ x + 5 – 5 < 0 – 5 and x – 5 + 5 < 0 + 5
⇒ x < –5 and x < 5
∴ x ∈ (–∞, –5) ∩ (–∞, 5)
However, (–∞, –5) ∩ (–∞, 5) = (–∞, –5)
Hence, x ∈ (–∞, –5)
Thus, the solution of the given inequation is (–∞, –5) ∪ (5, ∞).
