Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 2 of Exercise 15.2
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2
Solve each of the following system of inequations in R
2x – 7 > 5 – x, 11 – 5x ≤ 1
Given 2x – 7 > 5 – x and 11 – 5x ≤ 1
Let us consider the first inequality.
2x – 7 > 5 – x
⇒ 2x – 7 + 7 > 5 – x + 7
⇒ 2x > 12 – x
⇒ 2x + x > 12 – x + x
⇒ 3x > 12
⇒ x > 4
∴ x ∈ ( 4, ∞) (1)
Now, let us consider the second inequality.
11 – 5x ≤ 1
⇒ 11 – 5x – 11 ≤ 1 – 11
⇒ –5x ≤ –10
⇒ –x ≤ –2
⇒ x ≥ 2
∴ x ∈ (2, ∞) (2)
From (1) and (2), we get
x ∈ (4, ∞) ∩ (2, ∞)
∴ x ∈ (4, ∞)
Thus, the solution of the given system of inequations is (4, ∞).
