Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 24 of Exercise 15.1
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
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).
