Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 5 of Exercise 15.2
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5
Solve each of the following system of inequations in R
3x – 6 > 0, 2x – 5 > 0
Given 3x – 6 > 0 and 2x – 5 > 0
Let us consider the first inequality.
3x – 6 > 0
⇒ 3x – 6 + 6 > 0 + 6
⇒ 3x > 6
⇒ x > 2
∴ x ∈ ( 2, ∞) (1)
Now, let us consider the second inequality.
2x – 5 > 0
⇒ 2x – 5 + 5 > 0 + 5
⇒ 2x > 5
(2)
From (1) and (2), we get
Thus, the solution of the given system of inequations is
