Understanding the Absolute Value of a Number: Definition, Examples, and Applications

absolute value

The absolute value of a number, denoted by |x|, is the distance of that number from zero on a number line

The absolute value of a number, denoted by |x|, is the distance of that number from zero on a number line. In other words, it gives the magnitude or size of a real number without considering its sign.

To find the absolute value of a number:
1. If the number is positive, the absolute value is equal to the number itself. For example, |5| = 5.
2. If the number is negative, the absolute value is equal to the number with its sign changed to positive. For example, |-3| = 3.

Here are some examples to further explain the concept of absolute value:

Example 1:
Find the absolute value of -8.
Since -8 is a negative number, we change its sign to positive:
|-8| = 8

Example 2:
Find the absolute value of 11.
Since 11 is a positive number, the absolute value remains the same:
|11| = 11

Example 3:
Express the absolute value of 0.
Since 0 is neither positive nor negative, it is equal to zero:
|0| = 0

Absolute value can also be used when solving equations or inequalities. When solving an equation involving absolute value, it is important to consider both the positive and negative solutions.

For example, consider the equation |x| = 5.
This equation has two solutions:
1. x = 5, since the absolute value of 5 is 5; and
2. x = -5, since the absolute value of -5 is also 5.

In summary, the absolute value of a number is the magnitude or distance from zero on a number line. It disregards the sign of the number and provides a non-negative value.

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