Solving inequalities and graphing
Example Solve and graph 2  x + 2  > 6
Solution : i) Isolate the absolute value as  x + 2  > 3
ii) Setting the contents of the absolute value portion to + 3 and  3 or
+ (x + 2) > 3 and  ( x + 2) > 3
\ x + 2 > 3 and x+2 < 3
x > 1 and x < 5
The graph is
Example Solve and graph  2 x  1  £ 5
Solution :  2 x  1  £ 5
Therefore, setting the contents pf the absolute value portion as
( 2 x  1 ) £ + 5 and  ( 2 x  1) £ + 5
\ 2 x £ 6 and 2 x ³  5
\ x £ 3 and 2 x ³  4
x ³  2
\ x £ 3 and x ³ 2 or  2 £ x
Therefore ,  2 £ x £ 3 . . . required solution
= [  2 , 3 ]

Index
7.1 Definition 7.2
Simultaneous Equations 7.3
Inequations (Inequalities) 7.4
Absolute Values
Chapter 8
