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.