Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 3 of Exercise 15.2
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3
Solve each of the following system of inequations in R
x – 2 > 0, 3x < 18
Given x – 2 > 0 and 3x < 18
Let us consider the first inequality.
x – 2 < 0
⇒ x – 2 + 2 < 0 + 2
⇒ x < 2
∴ x ∈ ( 2, ∞) (1)
Now, let us consider the second inequality.
3x < 18
⇒ x < 6
∴ x ∈ (–∞, 6) (2)
From (1) and (2), we get
x ∈ (2, ∞) ∩ (–∞, 6)
∴ x ∈ ( 2, 6)
Thus, the solution of the given system of inequations is (2, 6).
