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Anonymous users2024-02-11The absolute value of x.
Geometric meaning refers to: the distance from a point x to a distant point on the number line.
Algebraic meaning means that if x>=0 then the absolute value of x is x, and if x<0 then the absolute value of x is -x
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Anonymous users2024-02-10We know that ,|x|The geometric meaning of is to represent the distance from the point (x) on the number line to the origin, thus |x -a|The geometric meaning of represents the distance from point (x) to point (a), likewise , |x +a|The geometric meaning of represents the distance from point (x) to point (a).Applying the geometric meaning of absolute value to solve some problems with absolute value can greatly simplify and intuitively solve the problem1. Solving the Absolute Value Equation Example 1 Solving the Equation |x -4 |+x +1|=5 .
The solution is known by the geometric meaning of the absolute value :|x -4 |+x +1|Represents the sum of the distance from point (x) to point (4) and the distance from point (x) to point (1) on the number line, and the distance between point A (-1) and point B (4) is equal to 5 when X is any point P on the line segment AB, then the sum of the distances from point P to points A and B is.
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Anonymous users2024-02-09The absolute value is the distance between the point where any number on the number line is located and the origin, so the absolute value of a number is not negative, and the absolute value of 0 is 0
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Anonymous users2024-02-08The difference between a number and its origin on the number line is the absolute value of this number.
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Anonymous users2024-02-07If a is a real number, |a|Denotes the absolute value of a. If a is plural, |a|Represents the modulo of a.
The modulo of complex numbers in mathematics. The value of the square root of the sum of the squares of the real and imaginary parts of a complex number is called the modulo of the complex number. The absolute value is the distance from the point to the origin of a number on the number line, which is used as "|".to represent.
b-a|or |a-b|Represents the distance between a point representing a and a point representing b on the number line.
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Anonymous users2024-02-06The absolute value is defined as: a number x, and if x is positive, then |x|=x。If x is 0, then |x|=0。If x is negative, then |-x|=x。The concept of absolute values can also be defined on complex numbers, ordered rings, and domains.
The generalization of the absolute value of real numbers occurs in a wide variety of mathematical settings, such as complex numbers, quaternions, ordered rings, fields, and vector space definitions. Absolute values are closely related to the concepts of size, distance, and norm in various mathematical and physical environments.
If the real number a ≠ 0, then there must be only one of the two symmetrical numbers a and -a that is greater than 0, and this number greater than 0 is called the absolute value of the number a and the number -a, which is denoted as |a|=|a|, the absolute value of 0 is 0. The absolute value of a number is never negative, there is no negative sign, and the absolute value of a number is expressed as |A certain number |. For all real numbers x:
If x is negative, |-x|=x, i.e. -x is a positive number; If x is not negative, |x|=x itself.
The absolute value of a number can be thought of as the distance between the point and the zero on the number line. For example, 3 is an absolute value of 3 and -3 at the same time.
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Anonymous users2024-02-05The absolute value is defined as: a number x, and if x is positive, then |x|=x。If x is 0, then |x|=0。If x is negative, then |-x|=x。The concept of absolute values can also be defined on complex numbers, ordered rings, and domains.
The generalization of the absolute value of real numbers occurs in a wide variety of mathematical circle settings, such as complex numbers, quaternions, ordered rings, fields, and vector spaces to define absolute values. Absolute values are closely related to the concepts of size, distance, and norm in various mathematical and physical environments.
If the real number a ≠ 0, then there must be only one of the two symmetrical numbers a and -a that is greater than 0, and this number greater than 0 is called the absolute value of the number a and the number -a, which is denoted as |a|=|a|, the absolute value of 0 is 0. The absolute value of a number is never negative, there is no negative sign, and the absolute value of a number is expressed as |A certain number |. For all real numbers x:
If x is negative, |-x|=x, i.e. -x is a positive number; If x is not negative, |x|=x itself is leaking. Orange hail beat.
The absolute value of a number can be thought of as the distance between the point and the zero on the number line. For example, 3 is an absolute value of 3 and -3 at the same time.
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Anonymous users2024-02-04When a is less than zero, the absolute value of a is -a.
A less than zero means that a is negative, and the absolute value of a negative number is its opposite.
In mathematics, absolute or modulus | x |, regardless of its sign, i.e., | x |x represents positive x, | x |x means negative x (-x is positive in this case), |0 | 0。For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be considered as the distance from zero.
Extended Materials. Both the algebraic and geometric significance of absolute values reveal the following related properties of absolute values:
1) The absolute value of any rational number is greater than or equal to the number of infiltration 0, which is the non-negativity of the absolute value.
2) There is only one number whose absolute value is equal to 0, which is 0.
3) There are two kinds of numbers whose absolute value is equal to the same positive number, and these two numbers are opposite to each other or equal.
4) The absolute values of two numbers that are opposite to each other are equal.
5) The absolute value of a positive number is itself.
6) The absolute value of a negative number is its opposite.
7) The absolute value of 0 is 0.
The above summary is for reference!
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Anonymous users2024-02-031. The meaning of 丨x丨 is to indicate the distance between the point x and the origin (regardless of the direction).
2. The meaning of 丨x丨 is that the absolute value of a number must be a non-negative number, i.e., |x|≥0；
3. The absolute value is the distance from the point to the origin of a number on the number lineto represent. b-a|or |a-b|Represents the distance between a point representing a and a point representing b on the number line. <>
Definition. On the number line, the distance from the point to the origin of a number is called the absolute value of the number, and the absolute value is called " |to represent. On the number line, the value that represents the distance between a point of number a and the point of number b, read as the absolute value of a-b, is denoted as |a-b|。 >>>More
1. When x<3a.
y=(a-x)(3a-x)=3a^2-4ax+x^2=(x-2a)^2-a^2 >>>More
In mathematics, absolute or modulus |
A non-negative value of x, regardless of its sign, i.e., | >>>More
f(x)= |x-1| +x+1|
f(-x)=|-x-1| +x+1| = |-x+1)| x-1)| = |x-1|+|x+1| = f(x) >>>More
This question is going to be discussed because we don't get to the absolute value sign that the number is exactly negative. The absolute value of a positive number is herself, and the absolute value of a negative number is her opposite. >>>More