different ways. – MAXWELL v . 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 cm. Your classroom can occupy atmost 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. . Inequalities Let us consider the following situations: (i) Ravi goes to market with ` to buy rice, which is available in packets of 1kg. The price of one packet of rice is ` .
If x denotes the number of packets of rice, which he buys, then the total amount spent by him is ` x . Since, he has to buy rice in packets only, he may not be able to spend the entire amount of ` . (Why?) Hence x < ... ( ) Clearly the statement (i) is not an equation as it does not involve the sign of equality.
(ii) Reshma has ` and wants to buy some registers and pens. The cost of one register is ` and that of a pen is ` . 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 ` ( x + y ) and we have x + y ≤ ... ( )