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 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 Index 7.1 Definition7.2 Simultaneous Equations7.3 Inequations (Inequalities)7.4 Absolute Values Chapter 8
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