| 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
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 + 2 x + 3 = 2 x =
2 x =
x =
|
7.1 Definition |
and - 
and 2 x = 
and x = 
. . . required solution