Strong and valid argument

Hey there guys.
I had a tough time getting to know the difference between a valid argument and a strong argument, but eventually go through with it. :D
First, I would like to define what a premises is, in my own words. A premises is a statement, or an event, that provides evidence or support to one's argument, for its conclusion. 
 Since a premises plays a major role in making an argument valid, a valid argument  is an argument which has to have all its premises true. It also has to have its conclusion true at the same time as well. If, either its premises or the conclusion is false, then the whole argument becomes invalid. In words of Epstein, a valid argument is "an argument, if there is no possible way for its premises to be true and its conclusion false at the same time" ( Epstein, Critical Thinking, 39).
Now, here is a simple example of  a valid argument :
2 + 2 = 4
Since, 1 + 1 = 2
Therefore, 1 + 1 + 1 + 1 = 4
Here the premises and the conclusion are true, all at the same time. A valid argument does not have to be a "good" argument as long as it is valid.

On the other hand, a strong argument is an argument where the premises and the conclusion are not true at the same time, but the premises cannot be questioned. In the words , Epstein states in his book that, a strong argument is "if there is some way, some possibility, for its premises to be true and its conclusion false" (Epstein, Critical Thinking, 40). Basically, an argument can be judged "strong" or "weak" only if the argument is invalid.
Here is the same example, but in terms of a strong argument :
2 + 2 = 4
Since, 1 + 1 = 2
Therefore, 1 + 1 + 1 = 4

The premises in this example are true and strong. Now, what I mean by "strong" is, that both my premises cannot be questioned. It is a clear cut fact. Nobody can prove my premises wrong. On the contrary, the problem with my argument is the conclusion. Regardless of my argument being invalid ( premises = true ; conclusion = false ), my premises are strong enough to make my entire argument a strong argument, but an invalid one nonetheless.
Hope this made sense :)