Michigan Algebra I Sept. 2012

There are two special cases that may arise when solving equations. They occur when the variable is eliminated from the equation, leaving a constant on both sides. If the resulting statement is true, such as 2 = 2, then any real number can be substituted for the variable and a true statement will be created. Therefore, the solution is all real numbers.

The other case occurs when the statement is false, such as 6 = 7, then any real number substituted in for the variable will create a false conclusion. Therefore, there is no solution.