Absolute Value Equations

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A mathematical statement, which shows that the absolute value of an expression is equal to the other

expression, is called an absolute value equation.

 
For example: -
 
If the expressions | 3 x – 5 | and x + 8 are equal, we write: | 3 x – 5 | = x + 8; which is an absolute value

equations.

 
Similarly other examples are: -
 
·         If the expression | x – 30 | is equal to 10, it is written as: | x – 30 | = 10

·         Absolute value of 7 subtracted from a number ( x ), equals 4, | x – 7 | = 4

·         An absolute value of a certain number ( x ) is multiplied by 4, equals 20, | 4 x | = 20

·         Absolute of x divided by 7, equals 2, | x / 7 | = 2


 
Question 1: - Find x when | x – 30 | = 10

 
Solution: - 

 | x – 30 | = 10


Case 1: -        +(x – 30) = 10

                         x – 30 = 10

                         x = 10 + 30

                         x = 40
 
Case 2: -        - (x – 30) = 10

                   -       x + 30 = 10

                   -       x = 10 – 30

                   -       = -20

                      x = 20

 
Question 2: - Find the value of x when | 4 x | = 20


 
Solution: -

                      | 4 x | = 20

Case 1:-         |4x| = 20

                      +4x = 20

                        x = 5

 
Case 2: -        -4x=20

                        x = -5

 

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