Today is our topic of discussion Concept of Inequality .
Concept of Inequality
We have acquired knowledge about equation and equality. But inequality also has an important and significant role in our practical life. At the end of this chapter, students will be able to-
- explain the inequality of one and two variables;
- form and solve simple inequalities of two variables;
- use inequalities to solve practical mathematical problems;
- solve inequalities of one and two variables graphically.
Suppose, there are 200 students in a class. Obviously it will be seen that, neither all the students are present in the class, nor all of them are absent always. If the number of present student is a in a particular day we can write 0 < x < 200. In a similar situation, we see that not all the invited persons are present in a ceremony. Clear conception of inequalities is needed in making dresses and other consumer goods.
Essential materials for constructing buildings, printing books and for many other similar works cannot be estimated exactly. So, initially we have to buy or collect those essential materials on the basis of idea. Therefore, it is understood that the knowledge of inequalities is very essential in our everyday life.
In case of real numbers,
a> b if and only if (a – b) is positive therefore (a – b)>0
a <b if and only if (a – b) negative therefore (a – b) <0
Some Laws Regarding Inequality:
1) a<b÷b> a
2) If a> b, for any c
a+c>b+c and a-c>b-c
3) If a > b, for any c
ac > bc and a/c > b/c when c> 0
ac< bc and a/c b/c< when c < 0
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