Prove 2+3(x-2)=5x-10 is incorrect My homework from the chapter of Order of Operations wants me to prove that the listed equations are incorrect. I am having a bit of a difficult time with this one, as the equation is correct when X=3. Am I going crazy, or is my teacher?
 A: Since this is from a chapter about order of operations, they probably want you to show that in general (for an arbritrary $x$), the LHS (left hand side) is not equal to the RHS. That is, they want you to give a reason as to why subtracting $2$ from an arbritrary quantity $x$, multiplying the result by $3$, and adding $2$ to the total is not the same as just multiplying that same $x$ by $5$ and subtracting $10$. 
There are various ways to show this. The easiest is to just find a counterexample. Try plugging in $0$ for $x$ (or any number other than $3$) on both sides an you will get a contradiction. This is sufficient to prove that this is not an (what we call) identity.
Another way to approach it is to solve for $x$. If this is really an identity, when we solve for $x$we should get something that suggests that the equation is true for all $x$,such as $x=x$. As you pointed out, when we solve for x we just get $x=3$, which means that there is just one unique solution, which in turn means that the equation is not true for arbitrary $x$.
