RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 15. Linear Inequations

Subject: Maths - Class 11th

Q. No. 8 of Exercise 15.2

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8

Solve each of the following system of inequations in R

5x – 1 < 24, 5x + 1 > –24

Given 5x – 1 < 24 and 5x + 1 > –24


Let us consider the first inequality.


5x – 1 < 24


5x – 1 + 1 < 24 + 1


5x < 25



x < 5


x (–∞, 5) (1)


Now, let us consider the second inequality.


5x + 1 > –24


5x + 1 – 1 > –24 – 1


5x > –25



x > –5


x (–5, ∞) (2)


From (1) and (2), we get


x (–∞, 5) (–5, ∞)


x (–5, 5)


Thus, the solution of the given system of inequations is (–5, 5).


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