Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 9 of Exercise 15.2
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9
Solve each of the following system of inequations in R
3x – 1 ≥ 5, x + 2 > –1
Given 3x – 1 ≥ 5 and x + 2 > –1
Let us consider the first inequality.
3x – 1 ≥ 5
⇒ 3x – 1 + 1 ≥ 5 + 1
⇒ 3x ≥ 6
⇒ x ≥ 2
∴ x ∈ (2, ∞) (1)
Now, let us consider the second inequality.
x + 2 > –1
⇒ x + 2 – 2 > –1 – 2
⇒ x > –3
∴ x ∈ (–3, ∞) (2)
From (1) and (2), we get
x ∈ (2, ∞) ∩ (–3, ∞)
∴ x ∈ (2, ∞)
Thus, the solution of the given system of inequations is (2, ∞).
