Absolute Value
The absolute value of a number, denoted by |x|, is the distance of that number from zero on the number line
The absolute value of a number, denoted by |x|, is the distance of that number from zero on the number line. In other words, it measures the magnitude or “size” of a number without considering its sign. The absolute value of a positive number is the number itself. For example, the absolute value of 3 is 3 (|3| = 3). Similarly, the absolute value of a negative number is the number without its negative sign. For example, the absolute value of -5 is 5 (|-5| = 5).
Formally, for any real number x, the absolute value is defined by:
|x| = x, if x ≥ 0 (x is positive or zero)
|x| = -x, if x < 0 (x is negative)
The concept of absolute value is often used in various mathematical contexts, such as solving equations, inequalities, and finding the distance between two points on a coordinate plane. It is an essential tool in calculus, algebra, and other branches of mathematics.
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