# How do you solve #13=5-13+3a#?

##### 1 Answer

There is only one correct answer, but there are many ways to get to that answer.

(There is only one London, England, but many ways to get there.)

**Here's one:**

Look for things the can be combined on the left of the equal sign. No, there's only a 13 there.

Look for things that can be combined on the right of the equal sign. Yes, I can do 5-13. So we write:

Often the words "is true if and only if" clutter up our solution, so we leave them out. I'll leave them out from here on.

Now, I want an

Our goal is to get

A lot of people like to put the unknown (

There are two ways of doing this. I think the simpler is to use the fact that

So now we want:

Look at the left side. Order of operations: if I picked a number for

To get

The whole process, without words explaining it looks like this:

.

.

The solution to the last equation is evident. The solution is

The solution to the first equation is also

I left some blank lines. For many people it becomes tiresome to include the steps below in red: (The middle 2 lines.)

**Here's a slightly different looking solution**

Again, it is obvious that the solution to the last equation is

The solution to the first equation is also