Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 15 of Exercise 15.2
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Solve each of the following system of inequations in R
, 2(2x + 3) < 6(x – 2) + 10
Given 
and 2(2x + 3) < 6(x – 2) + 10
Let us consider the first inequality.
⇒ 3(2x – 11) ≥ 4(4x – 18)
⇒ 6x – 33 ≥ 16x – 72
⇒ 6x – 33 + 33 ≥ 16x – 72 + 33
⇒ 6x ≥ 16x – 39
⇒ 16x – 39 ≤ 6x
⇒ 16x – 39 + 39 ≤ 6x + 39
⇒ 16x ≤ 6x + 39
⇒ 16x – 6x ≤ 6x + 39 – 6x
⇒ 10x ≤ 39
(1)
Now, let us consider the second inequality.
2(2x + 3) < 6(x – 2) + 10
⇒ 4x + 6 < 6x – 12 + 10
⇒ 4x + 6 < 6x – 2
⇒ 4x + 6 – 6 < 6x – 2 – 6
⇒ 4x < 6x – 8
⇒ 6x – 8 > 4x
⇒ 6x – 8 + 8 > 4x + 8
⇒ 6x > 4x + 8
⇒ 6x – 4x > 4x + 8 – 4x
⇒ 2x > 8
⇒ x > 4
∴ x ∈ (4, ∞) (2)
From (1) and (2), we get
∴ x ∈ ∅
Thus, there is no solution of the given system of inequations.
