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Concept

# Absolute value

The absolute value of a number is the distance between the number and $0$ on the number line. For example, the absolute value of $3,$ expressed as $|3|,$ is $3.$

The absolute value applies to negative numbers as well. The absolute value of $\text{-}3$ is the distance from $\text{-} 3$ to $0$ on the number line.

The absolute value of $3$ and $\text{-}3$ are equal, $|3|=|\text{-}3|=3.$ Therefore, the absolute value is the positive value of a number. Hence, the definition of the absolute value of $a$ is divided into two cases: the first where $a$ is positive or $0$, and the second when $a$ is negative. $|a|=\begin{cases}a,\quad a\geq 0 \\ \text{-} a,\quad a<0 \end{cases}$