Absolute Value Definition

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Definition: - The absolute value of any number a is denoted by the symbol | a |, and is defined by
            -a when a < 0
·         | a | = 0 when a = 0 and

·         | a | = a when a > 0

For example,

·         | a | = 5 (as 5 > 0),
·         | 0 | = 0 ,
·         | - 5 | = - ( - 5) = + 5 (As – 5 < 0),
·         | 3 – 5 | = | - 2 | = 2,
·         | 5 – 3 | = | 2 | = 2.
 
Examples of absolute value: -

Question 1: -  If | x – 8 | + 15 = 25, then find the value of x.

Solution: -| x – 8 | + 15 = 25
  | x – 8 | = 25 - 15
  | x – 8 | = 10
  x – 8 = 10
  x = 10 + 8
  x = 18

Question 2: -  If | x – 6 | = 20, find the value of x.
 
Solution: - | x – 6 | = 20
 x– 6 = 20
 x = 20 + 6
  x = 26

Question 3: - If | a + b | = | a – b| , find the value of b.
 
Solution:| a + b | = | a – b|
a + b = a –
 b + b = a – a
    2 b = 0
      b = 0 / 2
       b = 0



 

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