NCERT Book Class 11 Maths Linear Inequalities

6.1 Introduction In earlier classes, we have studied equations in one variable and two variables and also solved some statement problems by translating them in the form of equations. Now a natural question arises: ‘Is it always possible to translate a statement problem in the form of an equation? For example, the height of all the students in your class is less than 160 cm. Your classroom can occupy atmost 60 tables or chairs or both. Here we get certain statements involving a sign ‘<’ (less than), ‘>’ (greater than), ‘£’ (less than or equal) and ³ (greater than or equal) which are known as inequalities.

In this Chapter, we will study linear inequalities in one and two variables. The study of inequalities is very useful in solving problems in the field of science, mathematics, statistics, economics, psychology, etc.

6.2 Inequalities Let

us consider the following situations: (i) Ravi goes to market with ` 200 to buy rice, which is available in packets of 1kg. The price of one packet of rice is ` 30. If x denotes the number of packets of rice, which he buys, then the total amount spent by him is ` 30x. Since, he has to buy rice in packets only, he may not be able to spend the entire amount of ` 200. (Why?) Hence

30x < 200                                                     ... (1)

Clearly the statement (i) is not an equation as it does not involve the sign of equality. (ii) Reshma has ` 120 and wants to buy some registers and pens. The cost of one register is ` 40 and that of a pen is ` 20. In this case, if x denotes the number of registers and y, the number of pens which Reshma buys, then the total amount spent by her is ` (40x + 20y) and we have

40x + 20y £ 120                                          ... (2)

Please refer to attached file for NCERT Class 11 Maths Linear Inequalities