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That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity.

In fact, it should be true for all complex numbers as well.

Q: Why is the solution to an identity all real numbers?

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Definition: An equation is a statement that asserts that two mathematical expression are equal in value. When this is true for all values of the variables involved then it is called an identity, for example 2(x - 5) = 2x - 10. If you work at one side (or in both sides separately), you will find the same expression in both side., such that: 2x - 10 = 2x - 10 this is an identity, so that the solution of the equation is the set of all real numbers.

The identity property is the property that all numbers, real or imaginary, can be multiplied by 1 to obtain the same number; e.g., 14x1 = 14.

No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.

the domain is all real numbers and the range is all real numbers the domain is all real numbers and the range is all real numbers

the set of real numbers

Related questions

The result is all real numbers.

It is 1, as it is for all complex numbers - which includes real numbers.

no solution

It depends on the domain.

That is the identity property of multiplication for all rational numbers, or all real numbers or all complex numbers except (in each case) for 0.

Definition: An equation is a statement that asserts that two mathematical expression are equal in value. When this is true for all values of the variables involved then it is called an identity, for example 2(x - 5) = 2x - 10. If you work at one side (or in both sides separately), you will find the same expression in both side., such that: 2x - 10 = 2x - 10 this is an identity, so that the solution of the equation is the set of all real numbers.

By definition, an identity is true for all values of the variable. So the solution is the whole of the domain.

The identity property is the property that all numbers, real or imaginary, can be multiplied by 1 to obtain the same number; e.g., 14x1 = 14.

No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.No answer is possible. As soon as you have one valid line, all points that are not on that line cannot be part of the solution set. Therefore the solution set cannot be all real numbers.

The set of real numbers contains an additive identity - which is denoted by zero - such that, for all real numbers, x, x + 0 = 0 + x = x.

Closure: The sum of two real numbers is always a real number. Associativity: If a,b ,c are real numbers, then (a+b)+c = a+(b+c) Identity: 0 is the identity element since 0+a=a and a+0=a for any real number a. Inverse: Every real number (a) has an additive inverse (-a) since a + (-a) = 0 Those are the four requirements for a group.

All real numbers.