Michelle correctly solved a linear equation and the last line of her work was: 1 = 2
2 answers:
The equation has no solutions.
If, after a correct and legit manipulation, an equation turns into a false statement, than the original equation had no solutions.
It's easy to build an example: start with the equation
It is clear that this equation has no solutions: we can't get the same result by adding 1 and 2 to the same number! In fact, we can subtract x from both sides (which is a totally legit operation) and get
Which is a false statement, reflecting the fact that the equation had no solutions to begin with.
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