Remember when the result of an equation is a true statement, the solution is "all real numbers". It the result of the equation is a false statement, the solution is "empty set", "null set" or "no solution".
For example,
3x + 4 = -2x + 5x + 4
3x + 4 = 3x + 4
This is a true statement, so the solution for x is all real numbers.
In the equation -2x + x - 6 = 6x - 4 - 5x
we get
x - 6 = x - 4
subtract an x from both sides and we have
-6 = 4.
It's obvious that it is a false statement, therefore there is no solution.
Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied.definition of real numbers
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