Recognizing problem types

One of the reasons students of math struggle at test time is that they fail to quickly identify "problem types". Let's say you're taking an Algebra exam and you see something of the form 4x2 + 8x -5 = 18 and are required to solve it. You should either be thinking about factoring the equation or if that doesn't work easily, using the quadratic formula. Typically, once a student identifies the problem type, he or she is 80% of the way there. Then it's usually just standard arithmetic (watch your sign changes + or - ).

Solving math problems is really a process in itself and involves: assessment, identifying the problem type, looking for other complexities, i.e. there may be several steps along the way, doing the actual arithmetic and finally checking your answer for logic. Does it make sense that Fred took 16 hours to reach Chicago from New York? If it doesn't, go back and look at your problem -- you probably missed something.

Be disciplined in your approach and you will excel in your math courses!


I'm sure with more research I can figure this out but it has been a while almost 15 years since I've had to do algebra so I need a refresher to take a math assessment test.
How would you determine what kind of problem you are looking at? For example I am looking at 9-4(7x-6)=4x+27. There is a lot going on here and I'm sure I could figure it out if I knew what to do first! 

(btw that was an example from the practice test! I am not doing the actual test yet)
I will keep looking in the meanwhile, thanks for your help!
Hi Diana,
The important rule here is proper order of operations to be performed  ...  PEMDAS (parentheses, exponents, multiply, divide, add and subtract) in that order.  So, for your problem, distribute the "-4" through the paratheses first which will give you --
9-28x+24 = 4x+27
Now group like terms, i.e. whole numbers and "x" terms so ...
33-28x = 4x+27
Now group "x's" on the left side of the equation and whole numbers on the right by first subtracting 4x from BOTH sides so  ....
33-32x = 27
The subtract -33 from BOTH sides so  ....
-32x = -6
Divide BOTH sides by -32 so  ...
x = -6/-32 or +3/16 that's your answer!
Hope this helps.  Brian 


Brian D.

West Point Grad - Master Math & Improve SAT Score

20+ hours
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