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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Consider the attached tree.
You start from the root, and with each level you create a sub-branch for each of the choices you have.
So, the root has two children, white and multigrain bread.
Each of those children has three children, because you have three meat choices
Each of those children has two children, because you have two cheese choices.
Then, you identify all the sandwiches by choosing a leaf, and read the label that lead you there.
For example, leaf number 4 represents a sandwich with white bread, turkey and provolone.
