Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 1 of Exercise 15.2
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1
Solve each of the following system of inequations in R
x + 3 > 0, 2x < 14
Given x + 3 < 0 and 2x < 14
Let us consider the first inequality.
x + 3 < 0
⇒ x + 3 – 3 < 0 – 3
⇒ x < –3
∴ x ∈ ( –∞, –3) (1)
Now, let us consider the second inequality.
2x < 14
⇒ x < 7
∴ x ∈ (–∞, 7) (2)
From (1) and (2), we get
x ∈ (–∞, –3) ∩ (–∞, 7)
∴ x ∈ ( –∞, –3)
Thus, the solution of the given system of inequations is (–∞, –3).
