Eddy
One of the things that is confusing about a site like this is that each helper has his or her personal way to explain things. You have two choices: listen to one of us, or find what is common among us.
The great Khan asks “what is the FIND.”
Lev asks “what is the result.”
I say “what are the unknowns, how do you label them, and how do you express what you know about them in mathematical notation.”
All of those are really getting to the same point with different words. You are given in this problem a starting number that is UNKNOWN. You are asked to determine the number that is the result of doing certain operations on the unknown number. That result is, at least initially, also UNKNOWN. So lev and I immediately are talking about x and y or p and q or u and v. Two unknown numbers. Let’s arbitrarily pick x and y.
[math]y = \{ (x + 5)4 - 12\} \div 4.[/math]
Do you agree that is the translation of the game into mathematical notation?
Can you simplify that?
New topic. A lot of practical math involves sophisticated methods of guess and check. The field is called numerical methods. But the reason to study algebra is to avoid ANY KIND of guess and check. Moreover, this kind of problem cannot give ANY numerical result because we have two unknowns and only one equation. Algebra is a process for avoiding guess and check. Moreover, the answers proposed do not specify any numbers.
This is a different kind of problem. You are given a generic relationship and asked to find a simpler generic relationship. What SK calls the find here is not a number at all. The FIND is an equation.