What are the five steps to analyzing an argument?

Assuming you may be looking for Halpern's method from Critical thinking...? 


1. Make sure it IS an argument--needs to have premises and a stated or an implied conclusion. 

2. Diagram the argument, identifying premises and their relationship to the conclusion(s), plus any counterarguments, qualifiers, and assumptions. 
Counterarguments are statements that refute the conclusion the author favors. 
Qualifiers indicate restrictions on the conclusion--conditions under which the conclusion is or is not supported. 

Assumptions are statements (may be stated or implied) for which no support is offered. 
Multiple Premises may be arranged in a convergent or a chained structure. If chained, premises support other premises. Weak links undermine the whole chain.

3. Evaluate whether the premises are acceptable (seem to be true), consistent with one another, and relevant to the conclusion. 

4. If premises appeal to authority or experts, evaluate the credibility of these experts. Are they biased? Expert in the field? Evaluate the credibility of any evidence (such as research results) that is presented. 

5. Ask: What is missing? What counterarguments have not been considered?

Hope this helps
-Bumpsly

substitute y = 2x - 4 to x + 2y = 12:

x + 2(2x - 4) = 12     use distributive property

x + (2)(2x) + () = 12

x + 4x - 8 = 12     add 8 to both sides

5x = 20     divide both sides by 5

x = 4

put the value of x to the first equation:

y = 2(4) - 4

y = 8 - 4

y = 4

answer: x = 4 and y = 4