Rules of Equation Solution Outcomes
If you solve an equation and end up with; x = a number, then that is a solution, and the equation has a solution.
For example, you solve,
2x + 4 = 8
2x + 4 - 4 = 8 - 4
2x = 4
2x / 2 = 4 / 2
x = 2
Therefore, the equation has a solution
A number = a different number (e.g. 3=7) there are no solutions to the equations
For example, you solve,
2x + 5 = 2x - 7.
2x + 5 - 2x = 2x - 7 - 2x
5 = 7
Therefore, there is no solution to this equation
A number = the same number, (e.g. 5=5) then there are infinite solutions, every value of the variable is a solution to the equation
You solve 3(2x + 3) = 6x + 9
6x + 9 = 6x + 9
6x + 9 - 6x = 6x + 9 - 6x
9 = 9,
Therefore, there are infinite solutions