Edit the meaning of this paragraph.
Geometric meaning
On the number axis, the distance from the origin is called the absolute value of the number. For example, the distance between the point on the exponential axis and the origin is 5, so the absolute value is 5, which also represents the point and origin of 1.5 on the exponential axis.
Distance is 1.5, so the absolute value of 1.5 is 1.5.
Algebraic meaning
The absolute values of positive numbers and 0 are themselves, the absolute values of negative numbers are their opposites, and the absolute values of 0 are equal to the absolute values of the two opposites. The absolute value of a is represented by |a |, which is read as "the absolute value of a". Should be equal to less than sign, greater than or equal to sign, such as |-2 | read as the absolute value of negative two.
Edit this application.
The absolute value of a positive number is itself. The absolute value of a negative number is its reciprocal. , the absolute value is not negative ≥0. The absolute value of 0 is still zero. The absolute value of a special zero is both his own and his opposite number. Write | 0 | = 0 | 3 | = 3 | = 3 Two negative numbers are relatively large, and the absolute value of the big one is relatively small. For example, if | 2 (x- 1)-3 |+| 2 (y-4) | = 0. (| is the absolute value) Answer: 2 (x-1)-3 = 0x = 5/22y-8 = 0y = 4 The absolute values of a pair of opposites are equal: for example, the absolute value of +2 is equal to the absolute value of -2 (because they are equal in unit length from the origin on the number axis).
Edit the related properties of this paragraph.
No matter the algebraic or geometric meaning of absolute value, it reveals the following properties of absolute value: (1) The absolute value of any rational number is a number greater than or equal to 0, which is the nonnegativity of absolute value. (2) There is only one number whose absolute value is equal to 0, which is 0. (3) There are two numbers whose absolute values are equal to a positive number, and these two numbers are opposite. (4) The absolute values of two opposite numbers are equal.
Edit the absolute inequality of this paragraph.
(1) To solve the absolute value inequality, we must try to remove the absolute value symbol in the formula and convert it into a general algebraic type to solve it. (2) There are two main methods to prove absolute inequality: a) removing the absolute symbol and transforming it into general inequality proof: method of substitution, discussion method and flat method; B) Using the inequality: | a |-| b |≤| a+b |≤| a |+b |, the formula in absolute value is split and combined in this way to add and subtract terms, so that the formula to be proved is related to the known formula.
Edit this paragraph about the dispute of absolute value.
If we take 1 km south as+1 and 1 km north as-1, and find the absolute value of-1, the result is 1 km south? ! Obviously, there is something wrong here. The problem is that both positive and negative numbers are relative numbers, not absolute numbers, so the absolute value of relative numbers should be unsigned numbers, not positive numbers. Therefore, the unsigned number is not just a zero, there should be other unsigned numbers! So there is |-1 | =|+1| =1,where1is not a positive number, but an unsigned number like 0!