Determine the absolute value of an integer

Absolute value represents an integer’s distance from zero on the number line, so it is always nonnegative: the absolute value of a positive integer is itself, the absolute value of a negative integer is its opposite, and the absolute value of zero is zero. Opposite integers therefore have equal absolute values, a relationship that supports comparing magnitudes and interpreting distance in later work with equations and inequalities; this treatment is limited to integers, not absolute-value expressions involving variables.

Detailed Explanation: Determine the absolute value of an integer

Absolute value tells how far an integer is from $0$ on the number line. Distance is never negative, so an absolute value is always nonnegative.

If the integer is positive, its absolute value is the same number.
If the integer is negative, its absolute value is its opposite.
The absolute value of $0$ is $0$ .

Example: Find $\vert -7 \vert$

Locate $-7$ on the number line.
Count the distance from $-7$ to $0$ : it is $7$ units.
Since distance is positive, write:

\vert -7 \vert =7

So, the absolute value of $-7$ is $\boxed{7}$ . Notice that $7$ and $-7$ are opposite integers, but they have the same absolute value: $\vert 7 \vert = \vert -7 \vert =7$ .

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