If an equation simplifies to 0=0, what is the answer?

Question

anonymous · Answer

It's all good.
i.e. infinite solutions / all real numbers / etc.

anonymous · Answer

aren't all numbers real numbers?

anonymous · Answer

Nope, sorry to get into the very nitty gritty. But, point is, the expressions are directly equivalent, for all values, thus, for whatever the domain is (whatever numbers we can plug in for $x$), it has such as the solutions.

anonymous · Answer

solve for a 

0=a-a

and is the same as

0=0 

So infinite solutions.

anonymous · Answer

In other words, it's all good (unless your domain is restricted).

anonymous · Answer

Example:
$$\frac{1}{x}=\frac{2}{2x}$$
Cross-multiply the proportion:
$$2x=2x$$
Subtract 2x from both sides:
0=0, so the statement is true for all values of x except x=0 since that is not in the domain.
(would cause division by zero).