Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ Exercise 6.1 Book Name: **NCERT** Solutions Question 1: Solve 24 100 Solution 1: The given inequality is 24 100 24x 100 x , when (i) x is a natural number (ii) x is an integer x . 24x 100 [Dividing both sides by same positive number] 24 24 x 25 6 (i) It is evident that 1, 2, 3 and 4 are the only natural numbers less than Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3 and 4 1, 2,3, 4 Hence, in this case, the solution set is (ii) The integers less than 25 6 are …. 3, 2, 1,0,1,2,3,4 Thus, when x is an integer , the solutions of the given inequality are … Hence, in this case, the solution set is . 3, 2, 1,0,1, 2,3, 4 . 25 6 3, 2, 1,0,1,2,3,4 Question 2: Solve 12x 30, when (i) x is a natural number (ii) x is an integer Solution 2: The given inequality is 12x 30. 12x 30. 12x 30 12 12 5 x 2 [Dividing both sides by same negative number] 5 (i) There is no natural number less than 2 . Thus, when x is a natural number, there is no solution of the given inequality. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ (ii) The integers less than 5 2 are … 5, 4, 3 Thus, when x is an integer, the solutions of the given inequality are …., Hence, in this case, the solution set is ...., 5, 4, 3 . . 5, 4, 3 Question 3: Solve 5 3 7 , when (i) x is an integer (ii) x is a real number Solution 3: The given inequality is 5 3 7 5x 3 7 x 5x 33 7 3 5x 10 5x 10 5 5 x 2 x (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 …, 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 real numbers x which are less than 2. Thus, the solution set of the given inequality is x ,2 . . 4, 3, 2, 1,0,1 x 2, . that is, all Question 4: Solve 3x 8 2, when (i) x is an integer (ii) x is a real number Solution 4: The given inequality is 3 8 2 3x 8 2 3x 88 2 8 3x 6 x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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