Understanding Absolute Value: Definition and Examples in Mathematics

absolute value |x|

The absolute value of a number, denoted as |x|, is a mathematical operation that returns the non-negative value of a number

The absolute value of a number, denoted as |x|, is a mathematical operation that returns the non-negative value of a number. In other words, it gives the distance of the number from zero on the number line.

To understand absolute value, let’s consider a few examples:

Example 1:
If x = 5, then |x| = |5| = 5.
Here, the absolute value of 5 is 5 itself since it is already a non-negative number.

Example 2:
If x = -3, then |x| = |-3| = 3.
In this case, the absolute value of -3 is 3, which means it is 3 units away from zero on the number line.

Example 3:
If x = 0, then |x| = |0| = 0.
The absolute value of 0 is 0 itself since it is exactly at zero on the number line.

You can also think of absolute value as a way to “strip off” the negative sign from a number. Whether a number is positive or negative, the absolute value always gives a positive value.

Mathematically, the definition of absolute value can be represented using a piecewise function:

|x| = x, if x ≥ 0
|x| = -x, if x < 0 This means that if x is greater than or equal to zero, the absolute value of x is equal to x. However, if x is less than zero, the absolute value of x is equal to the negation of x. Absolute value plays an important role in various mathematical operations and problem-solving. It helps in calculating distances, determining magnitudes, solving equations and inequalities, and simplifying expressions.

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