Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 18 of Exercise 15.2
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18
Solve each of the following system of inequations in R
Given 
The above inequality can be split into two inequalities.
and 
Let us consider the first inequality.
⇒ 0 < –x
⇒ –x > 0
⇒ x < 0
∴ x ∈ (–∞, 0) (1)
Now, let us consider the second inequality.
⇒ –x < 6
⇒ x > –6
∴ x ∈ (–6, ∞) (2)
From (1) and (2), we get
x ∈ (–∞, 0) ∩ (–6, ∞)
∴ x ∈ (–6, 0)
Thus, the solution of the given system of inequations is (–6, 0).
