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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.

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Q: Why is the solution to an identity all real numbers?
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Continue Learning about Algebra

How can you tell when an equation has a solution of all real numbers?

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.


What is known about the lines of the equations in a system of equation when the solution set is 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.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.


What is the identity property for multiplications?

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.


Find the domain and range fx3x-2?

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


What is the set of numbers that includes all rational and all irrational numbers?

the set of real numbers