Concept of Inequality

Readers, Our Today's topic is   Concept of Inequality. It is important as Inequality related questions asked  in bank exams repeatedly.

First of all , when two values are equal ,

                  like  a=b

            then it is the concept of Equality .

When two values are not equal 

                 like  a ≠b

          then it is the concept of inequality

 ->  In inequality, there is two possibilities ,

     either a > b  or a < b

How to Solve Inequality Equation - Rules

A) we can add / subtract same number on both sides

like a-10>5

then adding 10 both side , give  result as a>15

B) we can switched both sides , for that we change the orientation of  inequality sign.

like a-10 > b-5 then b-5 < a-10

C) we can multiply/divide  by same ,  positive numbers on both sides

like 2a > 4 , divide by 2 both sides give result as  a > 2

D) we can multiply/divide  by same ,  negative  numbers on both sides , that time orientation of  inequality sign.must change.

like  -5a > 10 , divide both sides by -5 give result as a < -2

Important Rules(Summary)

1)  a > b and a>0 and b>0  then 1/a  <  1/b

2)  a>b and a<0 and b<0   then 1/a < 1/b   (same result as above as both are <0)

3) a>b  then a-b>0 and a=b +p   where p>0

4) a<b then a-b<0  and a=b - p where p>0

5) a>b  and k>0  then a+k>b+k

6) a>b and k>0 then ka > kb and a/k > b/k

7)a>b and k<0 then ka < kb and a/k < b/k

8) a>b then -a < -b

9) a<b and (x-a)(x-b) < 0 then a<x<b

10) a<b and (x-a)(x-b) <= 0 then a<= x <= b

11)  a<b and (x-a)(x-b) > 0 then x<a or x>b

12) a<b and (x-a)(x-b) >= 0 then x<= a or x>= b

Thanks .