Absolute Value Equation

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Absolute value always gives a positive number which is represented by modulus. Suppose x is a number then

the absolute value is represented by | x |.
| x | = x
| - x| = x


Examples of absolute value equation: -
·| a + b | = 5

·| 5 x + 2 | = 9
·| z | = 2
·| x + 2 y | + | 3 x – 9 y | = 10
 
Question 1: - Find the value of x;
| 5 x + 2 | = 9
Solution: - There will be two cases
Case 1: - + (5 x + 2) = 9
                 5x + 2 = 9
                 5 x = 9 – 2
                 5 x = 7
                 x = 7 / 5

Case 2: - - (5 x + 2) = 9
-       5 x – 2 = 9
-       5 x = 9 + 2
-       5 x = 11
-       x = 11/ 5
        x = -11 / 5
 
Question 2: - Find the value of x;

                       | 8 x – 2| = 2 x
Solution: -
Case 1: -      
  | 8 x – 2| = 2 x
  +(8 x – 2) = 2 x
    8 x – 2 = 2x
    8 x – 2 x = 2
    6 x = 2
    x = 2 / 6
    x = 1 / 3

Case 2: -       
| 8 x – 2| = 2 x
 -(8 x – 2) = 2x
 - 8 x + 2 = 2 x
 - 8 x – 2 x = - 2
 - 10 x = -2
    x = 2/10
    x=1/5
 

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