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Example:
Solve and graph the solution of the inequality 
Solution:
We have
 
 
 
or 
or 
Thus, the solution set is
 S.S 
OR
S.S 
The graph of the solution set.
Example:
Solve and graph the solution of the inequality  .
Solution:
We have
 
 
 
Here equality is not possible, because 13 is always greater than 12, in  . So, the solution of the given inequality is the set of all real numbers is  .
The solution can be written as 
Example:
Solve the inequality  .
Solution:
We have
 
 
 
Which is not possible, so the solution of the given inequality does not exist.
Example:
Find three consecutive positive odd integers whose sum is between 27 and 51.
Solution:
Let 'x',  ,  be the required three consecutive positive odd integers, then by the given condition
 
 
 
 
 
 
The odd number greater than 7 is 9.
If we take  then the other two odd numbers are
And if we take  , then the other two odd numbers are
And if we take  , then the other two odd numbers are
Thus, the required odd numbers are 9, 11, 13; or 11, 13, 15; or 13, 15, 17.
Note that 
All the sums 33, 39, 45 lie between the given numbers 27 and 51.
Example:
The length of a rectangle in one inch longer than twice the width. Express as an integer the maximum width of the rectangular when the perimeter is less than 80 inch.
Solution:
If 'x' is the required maximum width of the rectangle, then by the given condition,  is its length.
The perimeter of the rectangle is
Perimeter
 
 
 
 
 
   
This shows that  inch. Example:
Company A rents cars for Rs.600 a day and Rs.14 for every km driven. Company B rents cars for Rs.1200 a day and Rs.8 for every km driven. You want to rent a car for 5 days. How many km can you drive a company A car during the 5 days, if it is to cost less than a company B car?
Solution:
Let 'x' be the required number of kilometers, then by the given condition
Cost of Car A  Cost of Car B
 
 
 
 
 
  km.
This shows that it is less expensive to rent from company A if the car is driven les than 500 km.
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