4x - 2 = 4x - 2
What is the solution
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Since both sides of the equation are identical, any value for x would make the equality true. So the answer should be "all values of x".
I arrive at the same conclusion that the answer is the field of real numbers which is closed for this operation.
If you solve an equation and the variable disappears you end up with one of two results:
0 = 0
0 = 8 (or any number other than 0)
When you get one of these equations, ask yourself, "Is this always true, or is this never true?"
In the first case, the answer is "all real numbers." If you had two or more equations, it is also called a "dependent system."
In the second case, the answer is "no solution." If you had two or more equations, it is also called an "inconsistent system."
The all set of real numbers, noted R, is the solution to your equation which is in fact an identity!