RD Sharma - Mathematics

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, ∞).


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