NCERT Book Class 11 Maths Chapter 5 Linear Inequalities

Chapter 5
LINEAR INEQUALITIES

vMathematics is the art of saying many things in many
different ways. – MAXWELLv

5.1 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 ≥ (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.

5.2 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)