Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 17 of Exercise 15.2
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Solve each of the following system of inequations in R
Given 
and 
Let us consider the first inequality.
For this inequation to be true, there are two possible cases.
i. 11x – 2 > 0 and 7x – 1 < 0
⇒ 11x – 2 + 2 > 0 + 2 and 7x – 1 + 1 < 0 + 1
⇒ 11x > 2 and 7x < 1
However, 
Hence, this case is not possible.
ii. 11x – 2 < 0 and 7x – 1 > 0
⇒ 11x – 2 + 2 < 0 + 2 and 7x – 1 + 1 > 0 + 1
⇒ 11x < 2 and 7x > 1
However, 
Hence, 
(1)
Now, let us consider the second inequality.
For this inequation to be true, there are two possible cases.
i. x – 23 > 0 and x – 8 < 0
⇒ x – 23 + 23 > 0 + 23 and x – 8 + 8 < 0 + 8
⇒ x > 23 and x < 8
∴ x ∈ (23, ∞) ∩ (–∞, 5)
However, (23, ∞) ∩ (–∞, 5) = ∅
Hence, this case is not possible.
ii. x – 23 < 0 and x – 8 > 0
⇒ x – 23 + 23 < 0 + 23 and x – 8 + 8 > 0 + 8
⇒ x < 23 and x > 8
∴ x ∈ (–∞, 23) ∩ (8, ∞)
However, (–∞, 23) ∩ (8, ∞) = (8, 23)
Hence, x ∈ (8, 23) (2)
From (1) and (2), we get
∴ x ∈ ∅
Thus, there is no solution of the given system of inequations.
