What is absolute value?

Absolute value represents a number's distance from zero, denoted |x|. For positive numbers, the absolute value is the number itself; for negative numbers, it is the opposite; for zero, it is zero. |x| = x (x≥0), |x| = -x (x<0).

What is the geometric meaning of absolute value?

On a number line, |x| represents the distance from point x to the origin. |a-b| represents the distance between points a and b.

What are the properties of absolute value?

|a|≥0; |a|=0 if and only if a=0; |ab|=|a|×|b|; |a+b|≤|a|+|b| (triangle inequality); |-a|=|a|.

📏 Absolute Value Calculator

Calculate |x| with number line visualization

Value x

|-5|

-5 < 0, absolute value equals opposite 5

Number Line Visualization

-8

-7

-6

-5

-4

-3

-2

-1

-5

Absolute Value Properties

• |x| ≥ 0, absolute value is always non-negative

• |x| = 0 if and only if x = 0

• |-x| = |x|, opposite numbers have equal absolute values

• |x × y| = |x| × |y|

• |x + y| ≤ |x| + |y| (triangle inequality)

Absolute Value Calculator Guide

This calculator computes the absolute value |x| with a number line visualization. Enter any real number to calculate its absolute value.

Absolute value represents the distance of a number from zero on the number line — always non-negative. It's widely used in distance calculations, error analysis, and inequality solving.

Absolute Value Properties and Applications

Definition and properties:

- |x| = x (when x≥0) - |x| = -x (when x<0) - |x| ≥ 0 (always non-negative) - |-x| = |x| - |x×y| = |x|×|y| - |x+y| ≤ |x|+|y| (triangle inequality)

Examples: - |5| = 5 - |-7| = 7 - |0| = 0

This calculator is for reference only. Please verify results independently.

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