NCERT Solutions
Class 11 Maths
Linear Inequalities

Ex.6.1 Q.3
Solve 5x– 3 < 7, when
(1) x is an integer
(2) x is a real number
The given inequality is 5x– 3 < 7
=> 5x – 3 + 3 < 7 + 3
[3 is added both sides]
=> 5x < 10
=> x < 10 ÷ 5
=> x < 2
(1) 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}.
(2) When x is a real number, the solutions of the given inequality are given by x < 2, i.e., all real numbers x which are less than 2.
Thus, the solution set of the given inequality is x (–∞, 2).