Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 8 of Very Short Answer
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8
Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and 
.
Part I : 5x + 2 < 3x + 8
⇒ 2x < 6
⇒ x < 3
Part II : 
Case I : -3x + 6 < 0 and x – 1 > 0
⇒ x > 2 and x > 1
By taking intersection x ∈ (2, ∞)
Case II : -3x + 6 > 0 and x – 1 < 0
⇒ x < 2 and x < 1
By takin intersection x ∈ (-∞, 1)
Taking union of case I and case II, x ∈ (-∞, 1) (2, ∞)
We have to take intersection of part I and part II, we have
final answer i.e., x ∈ (-∞, 1) (2, 3)
