Question

Frank solved an equation and got the result x=x. Sarah solved the same equation and got 16=16. Frank says that one of them is incorrect because you cannot get different results for the same equation. What would you say to frank? If both results are indeed correct, explain how this happened.

Answer 1

Answer:

Frank, you're wrong!  x=x is a variable, where 12=12 is a specific number.  x can represent any number, even 12.  So Frank's answer is more general, whereas Sarah's answer is specific.  

Explanation:

2(x+12)+6=3(x+6)+(12-x)

2x+24+6=3x+18+12-x

2x+30=2x+30

2x+30-30=2x+30-30

2x=2x

x=x, or...

2x-2x+30=2x-2x+30

30=30