Absolute value is a mathematical concept, which represents the distance from a real number to the origin. Absolute value is defined as non-negative value of real number, that is, positive number or zero. The absolute value is usually represented by the symbol |. If you put a number in this symbol, you can get its absolute value.

Mathematical definition of absolute value of 1.

For the real number A, its absolute value is recorded as |a|, which is defined as | a | = a if a ≥ 0; If a

2. The essence of absolute value

The absolute value is always non-negative, that is, |a|≥0. If a=0, |a|=0. For any real number A, there is |a|=|-a|. The absolute value satisfies the trigonometric inequality, namely | a+b |≤| a |+b |.

3. Image representation of absolute value

The image of absolute value is usually V-shaped. For positive numbers, the image is located on the right side of the origin; For negative numbers, the image is to the left of the origin. Images intersect at the origin because |0=0.

4. Practical application

Absolute value plays an important role in many practical problems, such as distance measurement: absolute value indicates the distance between two points, whether on the number axis or on the plane. Temperature calculation: The temperature difference is usually expressed in absolute value, because the temperature can be negative. Financial field: absolute value can be used to express assets loss, profit and other indicators, whether positive or negative. Geometric problems: absolute values are often used to measure lengths, margins, etc. When solving geometry problems.

5. Solve absolute value equations sum inequality.

In algebra, we often encounter the solution of absolute value equations sum inequality. When solving absolute value equations, the equation should be divided into positive and negative cases according to the definition of absolute value. When solving absolute value inequality, we can use the properties of absolute value and combine the properties of inequality to deduce.

To sum up, absolute value is a basic mathematical concept, representing the distance from a real number to the origin. It has a clear mathematical definition and properties, and is widely used in mathematics and practical problems, including distance measurement, temperature calculation, financial field, geometric problems and so on. In algebra, solving absolute value equations and inequality is a common mathematical task, which needs to be analyzed and solved according to the definition and nature of absolute value.