Definition 3
The absolute value  a  of a Î R is defined to be equal to ^{ } . Thus =  a 
For example (i) If a = 2 then =   2  = 2
(ii) If a = 0 then =  0  = 0
We have some simple but important results
1 ®  a  b  =  b  a 
2 ®   a  £ a £  a 
3 ®  a . b  =  a  .  b 
4 ®
5 ®  a + b  £  a  +  b 
6 ®  a  b  >  a    b 
7 ®  a + b
 >  a    b

Example 1 Solve the inequality x + 3 < 7 x Î N
Solution :
x + 3 < 7 .. ( subtracting 3 from both sides)
x + 3  3 < 7  3
x < 4
Example 2 Solve and graph 3 £ < 5
Solution :
Breaking 3 £ < 5 into two inequalities as
3 £ and < 5
9 £ 2x  1 and 2x  1 < 15
9 + 1 £ 2x  1 + 1 and 2x  1 + 1 < 15 + 1
10 £ 2x and 2x < 16
£ and <
Thus the solution set is 5 £ x < 8 or [5, 8)
Graph :
