7.4 Absolute value
Definition: If x is a real number, then  x  is called the absolute value of x and it is the distance between x and 0.
For example,  0  = 0,  3  = 3 and  5  = 5
Now consider the distance between 2 and 3 is either 3  (2  =  5  = 5 . Thus if a and b are any two numbers, then  b  a  =  a  b 
Many equations and inequalities involving absolute values can be solved using this geometric aspect of absolute value .
Solving equations : To solve an equation involving absolute value
 Isolate the absolute value one side of the equation.
 Set its contents equal to both + and  the other side of the equation.
 Now solve both equations.
Example Solve 2  x   3 = 7
Solution : i) Isolating absolute value as
2  x   3 = 7
2  x  = 7 + 3
\ 2  x  = 10
\  x  = 5
ii) Set the contents of the absolute value equal to +5 and  5
i. e. x = + 5 and x =  5 . . . required solution
Example Solve 5  2 x + 3  + 3 = 20
Solution : i) Isolate the absolute value as
5  2 x + 3  = 17
 2 x + 3  =
ii) Setting the contents of the absolute value equal to + and  we get,
2 x + 3 = and 2 x + 3 = 
2 x = 3 and 2 x =  3
2 x = and 2 x =
x = and x = . . . required solution
