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