Solve 5x - 3 < 7 , when
(i) x is an integer (ii) x is a real number

Solution:

The given inequality is 5x - 3 < 7.

5x - 3 < 7

⇒ 5x - 3 + 3 < 7 + 3

⇒ 5x < 10

⇒ 5x/5 < 10/5

⇒ x < 2

(i) The integers less than 2 are ...., - 4, - 3, - 2, - 1, 0, 1.

Thus, when x is an integer,

the solutions of the given inequality are ...., - 4, - 3, - 2, - 1, 0, 1.

Hence, in this case, the solution set is {...., - 4, - 3, - 2, - 1, 0, 1}

(ii) When x is a real number,

the solutions of the given inequality are given by x < 2 that is all real numbers x which are less than 2.

Thus, the solution set of the given inequality is (- ∞, 2)

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NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 3

Solve 5x - 3 < 7 , when (i) x is an integer (ii) x is a real number

A linear inequation 5x - 3 < 7 is given. We have found that the solution set of the given inequality is (- ∞, 2)