Absolute Value Formula with Problem Solved Example

Absolute Value Formula

The absolute for some number is always represented as the |a|. The value can be shown by representing the distance between a and zero over a number line. The absolute value equation is the equation that contains some absolute value expression. Further, there are two possible techniques for absolute value inequalities. One with less than, |a|< b, and the other with greater than, |a|> b. They are solved differently.

Absolute Value Formula

Every time you are taking the absolute value for some number, it is given a positive value. Either the input is positive or negative, the output is always positive. For example, | 4 | = 4, and | –4 | = 4 also.

However, there should be some difference in the representation of two so that the third person can immediately identify that one negative number has been made positive through absolute value expressions. Here, are two possible cases to follow while working on absolute values.

  • If the value is positive or zero then it would be simply written as x = 4.
  • In case, x is a negative number then it would be written as x = ±4.

This is clear from the example above that both positive and negative values have become positive here and solving absolute value equations may be a little bit tricky sometimes but it is not impossible. With the right technique and approach, you can always reach the desired outcome as needed. Students should practice more problems to become efficient in solving absolute value equations on demand.

Absolute Value Solved Example

Question 1: What is the value of 2 | 5x – 1 | if x = – 2?
Solution:

2 | 5x – 1 | = 2 | 5 (-2) – 1 |
2 | 5x – 1 | = 2 | -10 – 1 |
2 | 5x – 1 | = 2 | -11 |
2 | 5x – 1 | = 2 | 11 |
2 | 5x – 1 | = 22

Question 2: Solve 4 | x – 2 | = 16
Solution:
4 | x – 2 | = 16
| x – 2 | = 16/4
| x – 2 | = 4
x – 2 = 4 or x – 2 = – 4
x = 4 + 2 or x = – 4 + 2
x = 6 or – 2


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