In solving a multi-step equation, a student ended up with 0x=4. She decided to divide both sides of the equation by 0 and got x = 0. How would you convince her that she has made a mistake?
0x = 4 is just 0 = 4, and 0 = 4 is not a true statement.
Another way to interpret it is that you have to divide by 0 to both sides to get x. However, any number divided by 0 is invalid --- there is no such thing.
